Andrew's move out of Royal Lodge may not happen until new year
There are also no plans to formally remove Andrew from the line of succession, the government says.
Why Sarah Ferguson, Beatrice and Eugenie can't escape the taint of family scandal
The scandal engulfing Andrew is of his own making but has had a profound impact on his immediate family.
'No inch here was spared': Hurricane Melissa destroys Jamaica town
The BBC’s Nada Tawfik reports from Black River, where the strongest storm to hit the country in modern history has left scenes of desperation.
Ex-sergeant major jailed for six months for sexual assault of soldier who took her own life
Michael Webber admitted sexually assaulting Jaysley Beck, 19, who later took her own life.
Just Stop Oil trio cleared over Stonehenge orange powder protest
The trio are cleared of all charges after citing human rights law in their defence.
Air India concludes phase 1 of retrofit of old planes
The 27 revamped narrowbodies will be utilised for as many as 3,024 weekly flights on 82 domestic and short-haul-international routes, the airline said
Even detours are jammed: Secunderabad motorists crawl through narrow, battered bylanes
Spillover from Paradise-Dairy Farm Road elevated corridor work turns Secunderabad’s inner roads into a commuter maze
Jharkhand migrant caught in crossfire in Saudi Arabia dies, Govt makes effort to bring back body
The youth identified as Vijay Kumar Mahato had been working in a private company as a tower line fitter for the last nine months.
Activist seeks probe into ‘fake encounter of Rohit Arya to cover up Government’s failures’
Advocate Nitin Satpute demands independent probe into hostage-taker’s death; questions raised over unpaid dues, police conduct, and government accountability.
Bihar polls: ‘People have decided to bring change,’ says Tejashwi Yadav | Interview
Mahagatbandhan will win as people want that those who talk about education, irrigation, medicine, jobs, and prompt action should form govt., says RJD leader and the Chief Ministerial face of the Opposition bloc; he says JD(U) will cease to exist after the polls as he rules out any tie-up with Nitish
What we know about Andrew losing titles and Windsor mansion
The language of Buckingham Palace's statement is "very brutal", royal historian Kelly Swaby tells the BBC.
King's statement on Andrew in full
The King's brother loses his title of prince and will now be known as Andrew Mountbatten Windsor.
Moment Question Time audience claps as they react to the news
A recording of the programme was interrupted on Thursday as the news broke.
Letting agent apologises for 'oversight' on Reeves rental licence
The company says its property manager offered to apply for the required licence but this never happened.
What the Reeves emails tell us in rental licence row
In several emails, the letting agent suggests they will apply for the licence on Reeves's behalf.
The internal rewiring of a grand old party: Congress focuses on DCCs for revival
As part of its newly launched leadership selection programme, Sangathan Srijan Abhiyan, the Congress is banking on empowered district-level leadership. After extensive screening and consultations, the 139-year-old party will appoint District Congress Committee presidents through a merit-based process across States. Sandeep Phukan explores the process and the criticism
Government relaxes green cover norms for industrial projects
Against a 33% green cover mandated earlier, industrial estates can earmark 10% for plantation while individual industries can have 15% greenbelt in their respective project areas
Chargesheet submitted in gang-rape of medical college student in West Bengal’s Durgapur
The chargesheet comes after 20 days of the horrific crime; charges have been pressed against the six accused for rape, gangrape, extortion, dacoity among other sections of BNS
Hospitals registration under ‘Karnataka Arogya Sanjeevini’ entrusted to Suvarna Arogya Suraksha Trust
As city sees a let-up in heavy rain, Highways Dept. begins restoration of battered roads
Afghan man charged after dog walker killed in London triple stabbing
A 22-year-old man has been charged after a dog walker was killed and two others injured in a stabbing in Uxbridge.
Chancellor admits breaking housing rules by renting out home
Rachel Reeves refers herself to the PM's ethics adviser after "inadvertently" renting out her family home without a licence.
Centrist liberals head for shock victory in Dutch election, exit poll says
Rob Jetten's D66 party celebrates, two years after his party languished in fifth place in the last vote.
Migrant sex offender given £500 after threat to disrupt deportation
Hadush Kebatu was given the money to avoid a "slower, more expensive process", Downing Street said.
Sudanese RSF militia killed many civilians at hospital, WHO chief and doctors say
Tedros Adhanom Ghebreyesus said he was "appalled" by reports that 460 civilians had been killed in el-Fasher.
2-day online camp offers positivity skill training for teens
MiTran Global’s Imparting Positivity Camp offers a two-day online programme for teens aged 11–17, blending academic skills with emotional resilience; register now at https://hub.mitranglobal.com/services/ipc
Japan PM Takaichi calls PM Modi, hopes for ‘golden chapter’ in ties with India
The conversation focused on the Quad, economic and defence cooperation; no clarity on summit dates yet
Campaigning heats up for Nuapada bypoll in Odisha as BJP, Cong., BJD vie for victory
As the constituency has a heterogeneous population, political parties cannot afford a one-size-fits-all strategy to win the trust of voters
Lookout notice issued to trace missing Suraj Lama
For Mayawati, a wasted opportunity
Her Lucknow rally was, in effect, old wine in an old bottle
Melissa's 185 mph winds at landfall means it could eclipse all storms the island has experienced before.
Israel strikes Gaza after accusing Hamas of ceasefire violations
Hamas denies it was behind an attack on Israeli forces inside an area of Gaza under their control and condemns the strikes.
Dog walker dies in triple stabbing as arrest made
A 22-year-old man was arrested at the scene and remains in police custody, the Met Police said.
Home Office has struggled to deal with crises, says Mahmood
The home secretary speaks to the BBC while overseeing a police operation in south London aimed at tackling illegal working.
Brigitte Macron's life 'deteriorated' after alleged cyber-bullying, daughter says
Tiphaine Auzière was testifying in the trial of ten people accused of cyber-bullying her mother, the French first lady.
SC orders NHRC to monitor Mental Health Authorities across the country
A petition had highlighted the plight of mentally-ill prisoners who were found chained at a “faith-based” asylum at Badayun in Uttar Pradesh
Why can't Bihar have Muslim CM, asks Owaisi
The Hyderabad MP lambasted the ruling NDA as well as the opposition INDIA bloc for allegedly "giving a raw deal" to the Muslim community
By declaring Tejashwi as CM face, INDIA bloc gave up little chance it had: Chirag
Mr. Paswan said the move has taken away even "a sliver of a chance" the opposition alliance had in the upcoming Bihar assembly elections.
Women indispensable for sustainable peace, says P. Wilson at UN Peacebuilding Commission
Mr. Wilson said India has shown through the deployment of women as peacekeepers that they can build trust in communities and “give hope to vulnerable populations”
Judges’ Quarters in Gudiyatham flooded due to lake breach
Migrant sex offender released due to human error, Lammy tells MPs
The justice secretary announced that an independent investigation has been launched after Hadush Kebatu was mistakenly released from prison.
Prince Andrew hosted Epstein, Maxwell and Weinstein at Royal Lodge
The trio were at Andrew's mansion in 2006 as part of his daughter Beatrice's 18th birthday celebrations.
King Charles heckled over Andrew and Epstein
The protester was met by vocal support for the King, including one woman who told him to "shut up".
Renters' Rights Bill becomes law - here's what it means for you
Sweeping new rules for renting in England receive royal assent - so what is changing?
Key figures at odds over collapse of China spy case
A parliamentary committee hears evidence about why the case against two men accused for spying for China was dropped.
All Temple-related construction at Shri Ram Janmabhoomi site completed, says Trust
The trust added that the construction of the seven pavilions has also been completed
Tripura online activist held for “abusing” State govt.
Madhavi Biswas, a resident of Pratapgarh in Agartala, has spoken about alleged corruption in the State government and lack of civic amenities.
CPI Ministers to boycott Cabinet demanding withdrawal from PM SHRI pact
CPI general secretary D. Raja calls Chief Minister Pinarayi Vijayan’s reasons for joining the contentious scheme unconvincing. Kerala government should have taken its cue from Tamil Nadu and moved the Supreme Court for unconditional and obligatory federal funding for education, he says
BJP hits out at Opposition over its stand on SIR 2.0
BJP national spokesperson Shehzad Poonawalla alleged that Congress and other Opposition parties are targeting the Election Commission and using the SIR as an excuse for the “impending losses” in the coming polls
Rajasthan, Uttar Pradesh all set for SIR of electoral rolls from today
While Uttar Pradesh has approximately 15.44 crore voters, Rajasthan has 5.48 crore registered voters
Epping migrant sex offender will be deported 'this week', says Justice Secretary Lammy
Hadush Kebatu was arrested in north London, two days after being mistakenly released from an Essex jail.
Inside Syria's jail for IS suspects as officials say attacks by group are rising
Kurdish counter-terrorism officials tell the BBC so-called Islamic State cells in Syria are regrouping and increasing attacks.
Egypt and Red Cross join search for hostage bodies in Gaza
Israel said the teams have been permitted to search beyond the so-called "yellow line" in the area controlled by its forces in Gaza.
Reform MP's comments about adverts 'racist', says Streeting
Sarah Pochin apologises for saying "it drives me mad when I see adverts full of black people, full of Asian people".
Two arrested over theft of jewels at Louvre museum in Paris
Four thieves broke into the world's most-visited museum in broad daylight, stealing eight items worth €88m (£76m; $102m).
Over 22,500 hectares of land taken up for mangrove restoration under MISHTI scheme, 85% of area in Gujarat
While 19,220 hectares of land under MISTHI scheme has been taken up in Gujarat, only 10 hectares of mangrove plantation has been taken up in West Bengal which accounts for about 42% of mangrove cover in country
President Murmu inaugurates Yashoda Medicity in Indirapuram
Other dignitaries included Union Minister of Defence Rajnath Singh, Chief Minister of Uttar Pradesh Yogi Adityanath and Union Minister of State for Health and Family Welfare Anupriya Patel, among others
Jaishankar holds talks with Malaysian PM, regional counterparts on sidelines of ASEAN summit
Mr. Jaishankar discussed the global and regional scenario with Singapore Counterpart Vivian Balakrishnan and deliberated on strengthening bilateral cooperation.
Being Bihari matter of pride for people of State now: Nitish
Hitting out at the INDIA bloc, without taking names of the Opposition leaders, the CM said that before 2005 (when the RJD was in power), there was complete anarchy in the State
Prepare for Janjatiya Gaurav Diwas, Centre urges States
In a letter, the government has asked States and UTs to ‘actively participate’ in “inauguration or benefit disbursal targeting tribal populations, launch of tribal-focused schemes, capacity building” and highlighting government schemes such as PM-JANMAN
Met urges Epping migrant sex offender to hand himself in
Hadush Kebatu has access to funds and sought help from the public, the Met Police says.
Trump raises tariffs on Canadian goods in response to Reagan advert
Saying that airing the advert was a hostile act, Trump announced an additional 10% "over and above what they are paying now".
'I am not done' - Kamala Harris tells BBC she may run for president again
The former US vice-president made her strongest suggestion to date she will make another bid for the White House
Lucy Powell elected Labour's deputy leader
She defeated Education Secretary Bridget Phillipson in a race triggered by Angela Rayner's resignation.
Tax rises could push food prices higher, warn supermarkets
The bosses of the UK's largest supermarkets warn the chancellor against imposing higher taxes on the industry.
Odisha rights panel orders Govt to rehabilitate Scheduled Caste families attacked twice
These families are not keen to return to their native village fearing backlash
West Bengal BJP urges Bangladeshi Hindu refugees to apply for citizenship under CAA ahead of 2026 polls
Union Minister Sukanta Majumdar said the party’s fight for 2026 is of “aar-paar” (two sides of a border). The statement assumes significance in light of the stark differentiation the saffron party has made between ‘infiltrators’ and ‘refugees’ from neighbouring countries, in the context of voter list revision and CAA camps respectively
Mehbooba moves PIL plea to shift J&K undertrials home
The former Chief Minister has approached the J&K High Court seeking the return of undertrial prisoners lodged in jails outside the Union Territory, citing violations of their right to fair trial and family access
Temples gearing up for Sura Samharam festivities in Chennai
Nearly 2,000 irrigation tanks in Tamil Nadu going beyond 75% storage
With the monsoon expected to yield higher rainfall this year, many more tanks may touch full level in the coming weeks
Manhunt after jailed Epping hotel asylum seeker mistakenly released
Ethiopian national Hadush Kebatu sparked nationwide protests after sexually assaulting a 14-year-old girl.
Watch: Video appears to show asylum seeker after accidental release from prison
A video shared online appears to show Hadush Gerberslasie Kebatu walking along Chelmsford high street.
Ukraine allies pledge to take Russian oil and gas off global market
A "coalition of the willing" meeting in London seeks to increase pressure on Russia to end its war in Ukraine.
Venezuela's Maduro says US 'fabricating war' as it deploys world's largest warship
The deployment of the USS Gerald R Ford marks a major escalation in what the US says is a campaign to target drug traffickers.
Men jailed over arson attack for Russia on Ukrainian business in London
Ringleader Dylan Earl, 21, was recruited by Russian mercenary group Wagner to attack a London warehouse sending aid to Ukraine.
Maiden flight of HTT-40 series production aircraft
The HTT-40 is an indigenous Basic Trainer Aircraft (BTA) designed and developed by Hindustan Aeronautics Limited (HAL) for the Indian Air Force (IAF)
CPI(M) seeks to ease tensions with CPI over PM-SHRI MoU
UDF, seemingly sensing a political opportunity, invited CPI to join the Opposition coalition. “The UDF will welcome CPI if the latter chooses to break ranks with the CPI(M)”, UDF convenor Adoor Prakash stated.
Trouble in ‘soy State’: Madhya Pradesh soybean farmers lose interest over multiple factors
Madhya Pradesh is India’s largest soybean producer, but young farmers are losing interest in farming, facing key issues such as improper implementation of minimum support price, seed quality, input cost and the possibility of the import of soybean and soybean meal from the United States. A.M. Jigeesh reports on a brewing crisis
Anganwadi workers’ union demands gratuity for retired employees
The government’s decision to provide gratuity to those who retire after 2023 should be modified and the gratuity should be applicable to all those who joined the service from 1975 and retired from 2011-12
BJP accuses Bengal Govt. of creating ‘fake citizens’ in border districts
The party claimed that these certificates are being used to create “fake voters” ahead of the Special Intensive Revision (SIR) of the electoral rolls
Met Police officers sacked for gross misconduct after BBC Panorama investigation
The chair of the panel called the conduct of Sgt Joe McIlvenny and PCs Philip Neilson and Martin Borg a "disgrace".
Former paratrooper found not guilty of all charges in Bloody Sunday murder trial
Thirteen people were shot dead and at least 15 others injured on Bloody Sunday in January 1972 at a civil rights demonstration in the Bogside area of Derry.
Search for new grooming inquiry head will 'take months'
The process to chose a chair for the inquiry was thrown into chaos when two leading the leading recused themselves from the job, the BBC understands.
'It's been an absolute dream': Tess Daly and Claudia Winkleman to leave Strictly
The pair have presented the show together since 2014 and said hosting the show had been "an absolute dream."
Rosenberg: Trump abandons carrot and wields stick over Putin in Ukraine talks
The BBC's Russia editor says Trump's decision to call off his Putin talks and impose oil sanctions will not go down well in Moscow.
30 lakh blooming chrysanthemums to fill grey tourism period of Kashmir with colours
Vedanta Group to invest ₹1,00,000 crore in Odisha
Vedanta Chairman Anil Agarwal met Chief Minister Mohan Charan Majhi and discussed proposed industrial projects
Cooch Behar SP shunted after assault against those bursting crackers draws condemnation
Dyutiman Bhattacharya, SP of Cooch Behar was accused of beating up several people, including children and women, for bursting firecrackers on Deepavali night (October 20) near his official residence.
Fresh Ponzi scam surfaces in West Bengal’s Asansol, ₹350 crore siphoned
LOP Suvendu Adhikari demanded the arrest of Tahsin Ahmed, the accused behind chit fund scam, return of money of the investors and investigation by SEBI-ED into the money trails.
Several including government officers injured in attack in Tripura’s Surma, Chief Minister blames Tipra Motha supporters.
Chief Minister Dr Manik Saha condemned the incident and said the administration has been directed to take swift action against those responsible
Trump says Putin talks 'don't go anywhere' as he imposes new sanctions
The US has announced new sanctions on Rosneft and Lukoil, Russia's two largest oil companies over continued fighting in Ukraine.
Harvey Willgoose killer sentenced to at least 16 years
Mohammed Umar Khan stabbed Harvey through the heart at Sheffield's All Saints Catholic High School.
No camera covered Louvre wall where jewel thieves broke in, director says
Laurence des Cars said there was only one camera pointing on the gallery which was robbed.
Child abuse expert pulls out of grooming inquiry over political 'point scoring'
Child exploitation expert Jim Gamble pulls out, after four women quit the inquiry's panel of survivors.
Migrant removed to France returns to UK on small boat
The man was sent to France under the 'one in, one out' deal but returned via the Channel on a small boat, the BBC understands.
Mega investment project for electric vehicle manufacturing coming up in Rajasthan
The plant, to be established at 65.56 acres of land, will play a crucial role in supplying affordable e-buses all over the country and promote the renewable energy sector
TMC says Union Govt not releasing funds to West Bengal amounts to deliberate financial strangulation
The West Bengal’s ruling party said that while funds have been made available to Maharashtra and Karnataka to douse their flood crisis, yet left food ravaged West Bengal has been left out in the cold.
Eyeing investment push, U.P. Government to open satellite investment promotion offices in five metro cities
U.P. Chief Minister Yogi Adityanath has already approved the proposal for restructuring ‘Invest U.P.’
CM demands SIR in Maharashtra, says problems with rolls
Fadnavis alleged that the Opposition had benefited the most from the duplication in electoral rolls
Protests erupt in West Bengal’s Kakdwip over ‘desecrated idol’
Leaders of the West Bengal BJP made serious allegations about the desecration of the idol, demanding immediate arrests and a probe into “administrative negligence.”
Trump says he did not want 'wasted meeting' after plan for Putin talks shelved
The comments by the US president come after plans to meet his Russian counterpart over the war in Ukraine were put on hold.
Third survivor quits grooming gang inquiry panel
"Elizabeth" says the process felt like "a cover-up", as she joins Fiona Goddard and Ellie Reynolds who quit the panel in protest on Monday.
The deal that means Prince Andrew can still afford to live in Royal Lodge
Controversies around Andrew have thrown a spotlight on his living arrangements and how he can fund his lifestyle.
Staff skipped checks and said a vulnerable young woman was safe. Days later, she was dead
A coroner says some of the care Cerys Lupton-Jones was given at a mental health unit was a "shambles".
Israel receives two bodies Hamas says are dead hostages
Two coffins were handed over by Hamas to the Israeli military via the Red Cross in Gaza on Tuesday.
WB BJP leadership alleges that Trinamool Govt is delaying Census in the State for political reasons
The BJP leadership in West Bengal has also alleged that fake birth and death certificates being issued from a state run hospital in Kharibari, an area bordering Bangladesh in North Bengal.
Priyank harks back to old video clip on ‘fund raising’ to hit out at BJP
Kharge alleged that both the BJP leaders had then discussed about payment of ₹1,800 crore to the party high command
Activists urge to reschedule, reroute Goddess Kali immersion procession for communal harmony in Cuttack
The timing of this proposed procession coincides with the Friday Namaaz at mosques in the city, they said
J&K Deputy CM eats his words on MP Ruhullah in the face of protests
There is growing isolation of Mr. Ruhullah within the NC’s top leadership, after the former’s public stand on issues like “reservation policy, arrested youth and the party’s unfulfilled manifesto”
As J&K Cabinet finalises report, Valley stakeholders frame 10-member committee on reservation issue
Representatives from different associations, open merit and general category representatives, and key stakeholders held a meeting in Srinagar
What has caused the outage at more than 1,000 companies?
The outage at Amazon services has impacted over 1,000 companies and affected millions of internet users.
University tuition fees in England to rise with inflation every year from 2026
Bridget Phillipson confirmed the plans for the next two years, with fees to increase automatically after that.
Met Police says it will no longer investigate non-crime hate incidents
The move comes as an investigation into Father Ted creator Graham Linehan is dropped, after his arrest over a post on X.
Maccabi Tel Aviv to decline any tickets offered to Villa match
Israeli club Maccabi Tel Aviv say they will not accept any ticket allocation from Aston Villa should the decision to ban their supporters from next month's Europa League match be overturned.
Hamas is a pale shadow of what it was - but it could yet reinvent itself
After governing with an iron rod for so many years, is Hamas really prepared to relinquish control in Gaza?
Truckers, commercial vehicle operators call for 4-day strike to protest bad roads in Mizoram
The blockade will be spearheaded by the Kolasib unit of the Mizoram Tipper Association (MTA) and Joint Action Committee (JAC) of drivers and owners of commercial vehicles in Kolasib town
33 nominations filed for bypolls in two Assembly segments in Jammu and Kashmir
The officials said 20 candidates, including eight independents filed their nominations from Budgam constituency where National Conference has fielded former minister Aga Syed Mehmood Al-Mousvi, BJP Aga Syed Mohsin Mosvi and PDP Aga Syed Muntazir Mehdi
Bihar Assembly polls: RJD's Sasaram candidate arrested after filing nomination
This was the third incident of contesting candidates of the constituents of INDIA bloc being arrested after filing their nomination papers.
Bihar Assembly polls: Filing of nomination papers over; INDIA bloc looks fractured
The Congress is contesting altogether 61 seats, five less than the number it had contested in 2020, when it had won only 19 and the dismal strike rate was blamed for the inability of Mahagathbandhan to win a majority
European Council approves ‘New Strategic EU-India Agenda’, efforts to conclude FTA
The council called on the European Commission to take forward the articulation and implementation of this ‘New Strategic EU-India Agenda’ on the basis of the priorities set out in the Joint Communication last month
Giuffre thought she might 'die a sex slave' at hands of Epstein and his circle, memoir reveals
The BBC obtained a copy of Virginia Giuffre's posthumous memoir ahead of its publication on Tuesday.
Everything we know about the Louvre jewellery heist
The world-famous museum in Paris was closed on Sunday after a masked gang raided one of its galleries.
Green Party leader defends wealth tax proposals
Zack Polanski says a new tax on the rich would tackle "the deep inequality in our society".
New V-level courses to be brought in for students after GCSEs
Ministers say new vocational courses will simplify the "confusing" options students have after GCSEs.
Why John Bolton case is more serious than those against other Trump critics
Bolton argues his case is an example of "weaponisation" but legal experts say the charges are serious.
Both YSRCP and TDP are equally destructive forces, alleges Congress leader Thulasi Reddy
While the YSRCP government left the State buried in debt, crime, liquor, drugs, and cannabis, the coalition government made things worse by taking record loans of ₹1.5 lakh crore in 16 months and burdening electricity users with ₹15,480 crore in surcharges
Container Road still a death trap for motorists
Traffic congestion on Goshree bridges, lack of adequate streetlights and alleged unscientific road and junction designs are cited by local people as major causes behind accidents on Container Terminal Road
TNSDA completes the first phase of underwater survey off the Poompuhar coast
A team of 10 divers carried out the survey, which began on September 20 and continued for 12 days. The department is planning one more phase of exploration when the sea conditions are favourable
Karnataka invites ETH Zurich’s quantum pioneer to next Quantum India Summit in Bengaluru
The State government has deepened its international scientific engagement with ETH Zurich — one of the world’s leading institutions in quantum science and technology — through a visit to the ETH Quantum Center and an invitation for its leadership to participate in the Quantum India Summit 2026 in Bengaluru.
New water pipeline from Sathanur dam to Tiruvannamalai nearing completion
Accuser's brother urges King to strip Andrew of prince title
Sky Roberts says he would like to see the King go a step further after Prince Andrew agreed to give up his other titles.
What difference will this really make for Andrew?
Prince Andrew has lost his titles - but will much of his life remain the same and will it stop the negative headlines?
No Kings protests draw huge crowds as anti-Trump rallies sweep across US
Protests are planned in over 2,500 cities across the US, including New York, DC, Atlanta and Los Angeles.
Israel receives two bodies that Hamas says are Gaza hostages
There is outrage in Israel that the armed group has not returned all deceased hostages from Gaza.
Tory MP reports deepfake defection video to police
Such political disinformation has the potential to corrupt democracy, says the Mid Norfolk MP.
How are India-Taliban relations changing? | Explained
Is India’s Afghanistan policy changing? What did the Muttaqi visit achieve? With India deciding to reopen its embassy in Kabul, is it inching closer to recognising a Taliban-led government? Did the restrictions imposed on women by the Taliban come up during talks?
Bhopal-based journalists released by Rajasthan Police, day after detention for ‘fake reports’ on Diya Kumari and ‘demanding money’
A spokesperson at ‘The Sootr’ said that the duo was released around 6 p.m. and “nothing concrete was found to prove the reports false”
West Bengal government seeks urgent repatriation of 11 migrant workers stranded in Oman
These migrant workers from Murshidabad, who had gone to work in Oman roughly 11 months back, were allegedly deceived by the recruiting agency and were left stranded without recourse
Bihar Assembly sat for average 29 days each year: ADR report
The report also showed 251 MLAs asked a total of 22,505 questions.; BJP MLA Arun Shankar Prasad asked the highest number of 275 questions, followed by Manohar Prasad Singh of the Congress, who posed 231 questions
Prashant Kishor: From backroom to ballot
The former political strategist, whose Jan Suraaj Party is contesting the coming Assembly elections in Bihar, seeks to disrupt the existing bipolar equations of the State and emerge as a new force
Prince Andrew is giving up his titles, including the Duke of York, he has announced in a personal statement.
After all those scandals, why did Andrew quit his titles now?
He has voluntarily given up his titles but was clearly under pressure to jump before he was pushed.
Government 'doing everything' to overturn Maccabi Tel Aviv fan ban
The Home Office said it is exploring what extra resources are required to allow fans to attend the Aston Villa match.
We're furious the 'Lip King' is selling weight-loss jabs, say dead mother's family
Alice Webb died last year after falling unwell following a non-surgical Brazilian butt lift carried out by Jordan Parke.
Red Cross retrieves body of dead hostage in Gaza, Israel says
The Israeli military says "a coffin of a deceased hostage" is now on the way to its troops in the territory.
CM Mamata clarifies on outsiders remark, says referred to a party, not people
West Bengal Chief Minister Mamata Banerjee alleged that Bhabanipur, the Assembly seat she has been representing, was being filled by ‘bohiragoto (outsiders)‘ in a planned manner.
13 of 17 State-run universities soon to have regular VCs, says Odisha Governor
Odisha Governor Hari Babu Kambhampati expresses concern over large vacancies in higher education institutes
Lucknow police proposes implementation of anti-digital arrest scam measures
The murky deaths in the Haryana Police
On October 7, an IPS officer from Haryana, Y. Puran Kumar, was found dead in Chandigarh. In a note supposedly written by him, Puran alleged caste-based discrimination by fellow officers. His death came a day after his personal security officer, Sushil Kumar, was booked in an extortion case. Days later, an Assistant Sub Inspector, Sandeep Lather, involved in Sushil’s arrest was also found dead. Vikas Vasudeva and Ashok Kumar report on the case
Three murder accused from Rajasthan held in Kolkata; one remains absconding
The three men are now in police custody and pending formal handover to the Rajasthan Police for further investigation
Trump says he will meet Putin in Hungary for Ukraine talks after 'very productive' call
The call comes a day before Ukrainian President Volodymyr Zelensky visits the White House.
'Wrong' to block Tel Aviv fans from Aston Villa match, says PM
Followers of the Israeli club will not be allowed to attend the Europa League game over safety concerns.
MI5 chief says China is daily threat to UK and voices frustration over spy case collapse
Sir Ken McCallum says the Security Service acted against Chinese activity in the last week, as a parliamentary inquiry is launched into the spy case.
Former Trump adviser John Bolton criminally indicted
Bolton is the third of the US president's political opponents to face charges in recent weeks.
Sam Fender wins 2025 Mercury Prize for album of the year
"I didn't think that was going to happen at all," the star says, as judges laud his "classic" album.
Congress government targeting RSS to divert public attention from its failures: BJP
Forest staff held for demanding bribe to release salary dues
Digvijaya Singh alleges SIR aimed at 'vote theft', says INDIA bloc will protest with proof
Singh accused the BJP of having 62 lakh voters removed from the electoral rolls in Bihar to influence assembly elections. He asserted, however, that the alliance in Bihar would still form the government.
BJP names star campaigners; PM, CMs in list
The list features a mix of prominent leaders and celebrities.
West Bengal Congress submits demands to CEO for modification of SIR process
The WBPCC’s memorandum listed out 16-point demands like the inclusion of electoral rolls since 2002 till that of the Assembly election in 2021 as probative evidence of eligibility and citizenship of a voter
Government publishes key witness statements in collapsed China spy case
Deputy national security adviser concluded China was "highly capable and conduct large-scale espionage operations against the UK".
Hamas returns two more bodies but says it cannot retrieve remaining dead hostages
The group's armed wing says it has returned all the bodies of hostages it can reach in the ruins of Gaza.
Funeral director admits fraud charges after inquiry into human remains at his premises in Hull
Robert Bush denied 30 counts of preventing lawful burials but admitted fraud charges.
'Worse than starting from scratch': How big is the task of rebuilding Gaza?
BBC Verify investigates the damage done by two years of war, which could take $70bn and decades to repair.
Giuffre accuses 'entitled' Andrew in posthumous book
Virginia Giuffre, who took her life earlier this year, gives her account of meeting Prince Andrew.
BJD slams Odisha CM for making his conversation with West Bengal rape survivor public
Despite recurrence of rape and gangrape incidents in Odisha over the last 15 months, the CM remained silent, charged Sulata Deo, BJD Rajya Sabha MP
Young and jobless: key demographic weighs claims and promises of parties
NDA government says it has been distributing lakhs of appointment letters for jobs in different sectors, with the Chief Minister promising at several events that ‘one crore more jobs will be given in the future’; Tejashwi says lakhs of jobs were provided during the 17 months of grand alliance rule
CPI(M) seeks judicial probe into Dalit IPS officer’s death
The party also called for the immediate suspension of all officials named by the late officer to prevent any interference in the investigation
Ekjut NDA, Ekjut Bihar, PM Modi tells party workers
The Prime Minister asserted the need to make every booth strong to ensure the party’s victory.
Chaos at Patna airport as Bihar Congress leaders are heckled by party cadre
Congress workers from the Bikram assembly constituency confronted the leaders when they arrived at the airport alleging corruption in ticket distribution.
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Q1: How much Pepsi at Rs. 6 a litre is added to 15 litre of ‘dew’ at Rs.10 a litre so that the price of the mixture be Rs. 9 a litre?
A. 5
B. 8
C. 10
D. None of these
Correct Answer: A
Solution: Let $x$ be the amount of Pepsi added. The total cost of 15 liters of dew is $15 \times 10 = \text{Rs. } 150$. The total cost of $x$ liters of Pepsi is $6x$. The total volume of the mixture is $15 + x$ liters. The total cost of the mixture is $150 + 6x$. The price of the mixture is Rs. 9 per liter. Therefore, $\frac{150 + 6x}{15 + x} = 9$
$$150 + 6x = 9(15 + x)$$
$$150 + 6x = 135 + 9x$$
$$150 - 135 = 9x - 6x$$
$$15 = 3x$$
$$x = \frac{15}{3} = 5 \text{ liters}$$
Therefore, 5 liters of Pepsi should be added.
Q2: In a municipal parking there are some two wheelers and rest are 4 wheelers. If wheels are counted, there are total 520 wheels but the incharge of the parking told me that there are only 175 vehicles. If no vehicle has a stepney, then the no. of two wheelers is :
A. 75
B. 100
C. 90
D. 85
Correct Answer: C
Solution: Let $x$ be the number of two-wheelers and $y$ be the number of four-wheelers. We know that the total number of vehicles is 175, so $x + y = 175$. The total number of wheels is 520, so $2x + 4y = 520$. We can solve this system of linear equations. From the first equation, we get $y = 175 - x$. Substitute this into the second equation: $2x + 4(175 - x) = 520$
$2x + 700 - 4x = 520$
$-2x = -180$
$x = 90$
Therefore, there are 90 two-wheelers.
Q3: In my pocket there are Rs. 25 consisting of only the denominations of 20 paise and 50 paise. Thus there are total 80 coins in my pocket.The no. of coins of the denomination of 50 paise is :
A. 30
B. 70
C. 50
D. 25
Correct Answer: A
Solution: Let $x$ be the number of 20 paise coins and $y$ be the number of 50 paise coins. We are given that the total number of coins is 80, so $x + y = 80$. The total value of the coins is Rs. 25, which is equal to 2500 paise. Therefore, $20x + 50y = 2500$. We have a system of two linear equations:
1) $x + y = 80$
2) $20x + 50y = 2500$
From equation (1), we can express $x$ as $x = 80 - y$. Substitute this into equation (2): $20(80 - y) + 50y = 2500$
$1600 - 20y + 50y = 2500$
$30y = 900$
$y = 30$
Therefore, there are 30 coins of 50 paise denomination. To verify, substitute $y = 30$ into $x = 80 - y$: $x = 80 - 30 = 50$. So there are 50 coins of 20 paise and 30 coins of 50 paise. Total coins: $50 + 30 = 80$ (Correct)
Total value: $(50 \times 20) + (30 \times 50) = 1000 + 1500 = 2500$ paise = Rs. 25 (Correct)
Q4: There are some shepherds and their sheep in a grazing field. The no. of total heads are 60 and total legs are 168 including both men and sheep. The no. of sheep is :
A. 18
B. 26
C. 24
D. 36
Correct Answer: C
Solution: Let $x$ be the number of shepherds and $y$ be the number of sheep. Each shepherd has 2 legs and each sheep has 4 legs. We can set up a system of two linear equations based on the given information:
$$ x + y = 60 $$
$$ 2x + 4y = 168 $$
We can solve this system of equations using substitution or elimination. Let's use elimination. Multiply Equation 1 by -2:
$$ -2x - 2y = -120 $$
Now add this modified Equation 1 to Equation 2:
$$ (-2x - 2y) + (2x + 4y) = -120 + 168 $$
$$ 2y = 48 $$
$$ y = 24 $$
Therefore, there are 24 sheep. Substitute $y = 24$ back into Equation 1 to find $x$:
$$ x + 24 = 60 $$
$$ x = 36 $$
There are 36 shepherds and 24 sheep. The question asks for the number of sheep.
Q5: In the 75 litres of mixture of milk and water, the ratio of milk and water is 4 :1. The quantity of water required to make the ratio of milk and water 3:1 is :
A. 1 litre
B. 3 litres
C. 4 litres
D. 5 litres
Correct Answer: D
Solution: Let the quantity of milk in the mixture be $4x$ litres and the quantity of water be $x$ litres. Total quantity of mixture = $4x + x = 5x$ litres. Given that the total quantity of mixture is 75 litres, we have $5x = 75$. Therefore, $x = 15$ litres. Quantity of milk = $4x = 4 \times 15 = 60$ litres. Quantity of water = $x = 15$ litres. Let $y$ litres of water be added to make the ratio of milk and water 3:1. The quantity of milk remains the same, which is 60 litres. The quantity of water becomes $15 + y$ litres. The new ratio of milk to water is $60 : (15 + y) = 3 : 1$. We can set up a proportion:
$$ \frac{60}{15 + y} = \frac{3}{1} $$
Cross-multiplying, we get:
$60 = 3(15 + y)$
$60 = 45 + 3y$
$3y = 60 - 45$
$3y = 15$
$y = 5$
Therefore, 5 litres of water needs to be added.
Q6: A car agency has 108 cars. He sold some cars at 9% profit and rest at 36% profit. Thus he gains 17% on the sale of all his cars. The no. of cars sold at 36% profit is :
A. 25
B. 32
C. 35
D. 75
Correct Answer: B
Solution: Let $x$ be the number of cars sold at 9% profit and $(108-x)$ be the number of cars sold at 36% profit. The total profit is 17% of 108 cars. Let $CP$ be the cost price of each car. The total cost price is $108CP$. $$108CP \times 1.17 = 126.36CP$$
The total selling price is $126.36CP$. The selling price from cars sold at 9% profit is $xCP \times 1.09 = 1.09xCP$. The selling price from cars sold at 36% profit is $(108-x)CP \times 1.36 = 146.88CP - 1.36xCP$. Therefore, $1.09xCP + 146.88CP - 1.36xCP = 126.36CP$
$$146.88CP - 0.27xCP = 126.36CP$$
$$0.27xCP = 20.52CP$$
$$x = \frac{20.52}{0.27} = 76$$
The number of cars sold at 36% profit is $108 - 76 = 32$.
Q7: Rs. 69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy received twice the paise as each girl received. The no. of girls in the class is :
A. 92
B. 42
C. 33
D. 23
Correct Answer: A
Solution: Let the amount received by each girl be $x$ paise. Then each boy received $2x$ paise. Each girl received 50 paise less than a boy, so $x + 50 = 2x$. Solving for $x$, we get $x = 50$ paise. Therefore, each girl received 50 paise and each boy received 100 paise ($2 \times 50 = 100$). Let the number of girls be $g$ and the number of boys be $b$. The total number of students is 115, so $g + b = 115$. The total amount distributed is Rs. 69, which is 6900 paise. So, $50g + 100b = 6900$. We have a system of two equations:
$$g + b = 115$$
$$50g + 100b = 6900$$
From the first equation, $b = 115 - g$. Substitute this into the second equation:
$50g + 100(115 - g) = 6900$
$50g + 11500 - 100g = 6900$
$-50g = -4600$
$g = 92$
Therefore, there are 92 girls.
Q8: A butler stole wine from a butt of sherry containing 50% of spirit, then he replenished it by different wine containing 20% spirit. Thus there was only 30% strength (spirit) in the new mixture. How much of the original wine did he steal?
A. 1 / 3
B. 2 / 3
C. 1 / 2
D. 1 / 4
Correct Answer: B
Solution: Let $x$ be the amount of wine stolen. The original mixture contained 50% spirit. After $x$ amount is stolen, the remaining spirit is $0.5(1-x)$. The butler then adds $x$ amount of 20% spirit wine. The total volume remains 1. The new mixture contains 30% spirit. Therefore, we can set up the equation:
$$0.5(1-x) + 0.2x = 0.3(1)$$
Solving for $x$: $0.5 - 0.5x + 0.2x = 0.3$. This simplifies to $0.2 = 0.3x$. Therefore, $x = \frac{0.2}{0.3} = \frac{2}{3}$. The butler stole $\frac{2}{3}$ of the original wine. To express this as a percentage, $\left(\frac{2}{3}\right) \times 100\% \approx 66.67\%$. However, the question asks how much of the original wine, not percentage. Therefore, the answer is $\frac{2}{3}$ or approximately 66.67% of the original wine. Let's assume the butt contained 1 unit of wine. Then the butler stole $\left(\frac{2}{3}\right)$ units of wine.
Q9: In what proportion water be mixed with spirit to gain 12.5% by selling it at cost price?
A. 3 : 5
B. 1 : 8
C. 2 : 7
D. 1 : 9
Correct Answer: B
Solution: Let the cost price of the spirit be Rs. $100$ per liter. To gain $12.5\%$, the selling price should be Rs. $112.5$. However, the spirit is sold at the cost price, implying that the seller is selling less spirit than a liter. Let $x$ liters of spirit be sold for Rs. $100$. Then, the selling price per liter = $\frac{100}{x}$. The gain is $12.5\%$, therefore, the selling price is $112.5\%$ of the cost price. We have: $\frac{100}{x} = 1.125 \times 100$
$\frac{100}{x} = 112.5$
$x = \frac{100}{112.5} = \frac{1000}{1125} = \frac{8}{9}$
This means that $\frac{8}{9}$ liters of spirit are sold as 1 liter. The quantity of water added is $1 - \frac{8}{9} = \frac{1}{9}$ liters. The proportion of water to spirit is $\frac{1/9}{8/9} = \frac{1}{8}$. Therefore, the proportion of water to spirit is $1:8$.
Q10: Mr. Mittal purchased two steel factories, one in India and other one in Malaysia for total Rs. 72 crores. Later on he sold the Indian factory at 16% profit and Malasian factory at 24% profit. Thus he gained a total profit of 19%. The selling price of Indian factory is:
A. 45 crore
B. 52.2 crore
C. 8.55 crore
D. Cannot be determined
Correct Answer: B
Solution: Let the cost price of the Indian factory be $x$ crores and the cost price of the Malaysian factory be $(72-x)$ crores. The selling price of the Indian factory is $1.16x$ crores ($16\%$ profit). The selling price of the Malaysian factory is $1.24(72-x)$ crores ($24\%$ profit). Total selling price = $1.16x + 1.24(72-x) = 1.19 \times 72$ ($19\%$ total profit)
$$1.16x + 89.28 - 1.24x = 85.68$$
$$-0.08x = 85.68 - 89.28$$
$$-0.08x = -3.6$$
$$x = 45$$
Selling price of Indian factory = $1.16x = 1.16 \times 45 = 52.2$ crores
Q11: In a 25 litre mixture of milk and water, the water is only 20%. How many litres of water is required to increase the percentage of water to 90%?
A. 45 litre
B. 70 litre
C. 115 litre
D. 175 litre
Correct Answer: D
Solution: Step 1: Calculate the initial amount of water: 20% of 25 litres = $\frac{20}{100} \times 25 = 5$ litres. Step 2: Calculate the initial amount of milk: 25 litres - 5 litres = 20 litres. Step 3: Let $x$ be the amount of water added. The total volume becomes $25 + x$ litres. Step 4: The amount of water becomes $5 + x$ litres. Step 5: The new percentage of water is 90%, so we set up the equation: $\frac{5 + x}{25 + x} = \frac{90}{100}$. Step 6: Simplify the equation: $100(5 + x) = 90(25 + x)$
Step 7: Expand: $500 + 100x = 2250 + 90x$
Step 8: Solve for $x$: $10x = 1750$
Step 9: $x = 175$ litres. Therefore, 175 litres of water needs to be added.
Q12: In a class of 30 students, the average weight of boys is 20 kg and the average weight of the girls is 25 kg. The fraction of boys out of the total students of the class is :
A. 4 / 5
B. 5 / 6
C. 3 / 4
D. Data Inadequate
Correct Answer: D
Solution: Let $b$ be the number of boys and $g$ be the number of girls. We know that $b + g = 30$. The total weight of boys is $20b$ kg, and the total weight of girls is $25g$ kg. The average weight of the class is a weighted average of the boys' and girls' average weights. Let's assume the average weight of the class is $x$. We don't need to calculate $x$ directly to solve the problem. Using the concept of alligation, we can set up a ratio:
$$ \frac{25 - x}{x - 20} = \frac{b}{g} $$
We also know that $\frac{b}{30}$ is the fraction of boys. We can use another approach. Let the total weight of the class be $W$. Then:
$$ W = 20b + 25g $$
The average weight of the class is $\frac{W}{30}$. We don't need this value directly. Let's use the weighted average concept to find the fraction of boys. Let $f$ be the fraction of boys. Then $(1-f)$ is the fraction of girls. The average weight of the class can be expressed as:
Average = $f \times 20 + (1-f) \times 25$
We don't need to solve for the average. We are given that the total number of students is 30. Therefore:
$f = \frac{b}{30}$ and $(1-f) = \frac{g}{30}$
We can't solve for $f$ directly using this method without more information. However, we can use the given information to find the ratio. Let's reconsider the alligation approach. We don't have the overall average. Instead, we are looking for $\frac{b}{30}$. Let's use another approach:
Suppose we assume an overall average weight. Let’s say 22 kg. Using the alligation method:
$$ \frac{25-22}{22-20} = \frac{3}{2} $$ This represents the ratio of girls to boys. So, the ratio is $g:b = 3:2$. This means $g = 3k$ and $b = 2k$ for some integer $k$. Since $g + b = 30$, we have $5k = 30$, which means $k = 6$. Therefore, $b = 12$ and $g = 18$. The fraction of boys is $\frac{b}{b+g} = \frac{12}{30} = \frac{2}{5}$
Q13: The price of petrol is Rs. 60 per litre and the price of spirit is Rs. 40 per litre. In what ratio the petrol and spirit be mixed such that the profit after selling the mixture at Rs. 75 per litre be 25%?
A. 1 : 1
B. 3 : 2
C. 5 : 1
D. Such a mixture is not possible
Correct Answer: D
Solution: Let the ratio of petrol to spirit be $x:y$. Cost price of petrol = $60x$
Cost price of spirit = $40y$
Total cost price = $60x + 40y$
Selling price of mixture = $75(x+y)$
Profit = Selling Price - Cost Price = $75(x+y) - (60x + 40y) = 15x + 35y$
Profit percentage = $\frac{\text{Profit}}{\text{Cost Price}} \times 100 = 25\%$
Therefore, $\frac{15x + 35y}{60x + 40y} = 0.25$
Solving the equation:
$15x + 35y = 0.25(60x + 40y)$
$15x + 35y = 15x + 10y$
$25y = 0$
This equation implies that there's an error in the question's formulation, as it leads to $y=0$, which is not a valid ratio. The problem likely lies in the profit percentage calculation or the given selling price. Let's assume the profit is 25% of the cost price. Let's re-examine. Let the ratio be $x:y$. Cost price of mixture = $\frac{60x + 40y}{x+y}$
Selling price = 75
Profit = $75 - \frac{60x + 40y}{x+y}$
Profit percentage = 25%
$\frac{75 - \frac{60x + 40y}{x+y}}{\frac{60x + 40y}{x+y}} = 0.25$
$75(x+y) - (60x + 40y) = 0.25(60x + 40y)$
$75x + 75y - 60x - 40y = 15x + 10y$
$15x + 35y = 15x + 10y$
$25y = 0$
This still leads to an invalid solution. There must be a mistake in the question's parameters. A valid solution cannot be obtained with the given information.
Q14: A trader sells total 315 TV sets. He sells black and white TV sets at a loss of 6% and colour TV sets at a profit of 15%.Thus he gains 9% on the whole. The no. of B/ W TV sets, which he has sold, is :
A. 126
B. 216
C. 135
D. 90
Correct Answer: D
Solution: Let $x$ be the number of black and white TV sets and $y$ be the number of color TV sets. Total TV sets sold = $x + y = 315$ (1)
Let $CP_{bw}$ be the cost price of one black and white TV set and $CP_c$ be the cost price of one color TV set. We assume that $CP_{bw} = CP_c = CP$ (for simplification, this doesn't affect the final answer because we're only dealing with ratios). The selling price of black and white TV sets = $CP \times (1 - 0.06) = 0.94 CP$
The selling price of color TV sets = $CP \times (1 + 0.15) = 1.15 CP$
Total cost price = $x \times CP + y \times CP = (x+y) \times CP = 315 \times CP$
Total selling price = $0.94x \times CP + 1.15y \times CP$
Overall profit is 9%, so total selling price = $315 \times CP \times 1.09 = 343.35 \times CP$
Therefore, $0.94x \times CP + 1.15y \times CP = 343.35 \times CP$
Dividing by $CP$, we get $0.94x + 1.15y = 343.35$ (2)
Substitute (1) into (2): $y = 315 - x$
$0.94x + 1.15(315 - x) = 343.35$
$0.94x + 362.25 - 1.15x = 343.35$
$-0.21x = -18.9$
$x = \frac{18.9}{0.21} = 90$
Therefore, the number of black and white TV sets sold is 90.
Q15: The average age of boys in class is 16.66, while the average age of girls is 18.75. Thus the average age of all the 40 students of the class is 17.5. If the difference between the no. of boys and girls is 8, then the no. of girls in the class is :
A. 12
B. 16
C. 18
D. Data Inadequate
Correct Answer: B
Solution: Let $b$ be the number of boys and $g$ be the number of girls. Total number of students = $b + g = 40$ (1)
Total age of boys = $16.66b$
Total age of girls = $18.75g$
Total age of all students = $16.66b + 18.75g$
Average age of all students = $\frac{16.66b + 18.75g}{40} = 17.5$
$16.66b + 18.75g = 17.5 \times 40 = 700$ (2)
The difference between the number of boys and girls is 8. $b - g = 8$ or $g - b = 8$
Case 1: $b - g = 8 \Rightarrow b = g + 8$. Substitute in (1): $g + 8 + g = 40 \Rightarrow 2g = 32 \Rightarrow g = 16, b = 24$
Substitute in (2): $16.66 \times 24 + 18.75 \times 16 = 400 + 300 = 700$. This is correct. Case 2: $g - b = 8 \Rightarrow g = b + 8$. Substitute in (1): $b + b + 8 = 40 \Rightarrow 2b = 32 \Rightarrow b = 16, g = 24$
Substitute in (2): $16.66 \times 16 + 18.75 \times 24 = 266.56 + 450 = 716.56$. This is incorrect. Therefore, the number of girls is 16.
Q16: The ratio of water and alcohol in two different containers is 2: 3 and 4: 5 In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7 : 5?
A. 7 : 3
B. 5 : 3
C. 8 : 5
D. 2 : 7
Correct Answer: B
Solution: Let the ratio of water and alcohol in container 1 be $2:3$. This means for every 5 units of mixture, there are 2 units of water and 3 units of alcohol. The fraction of alcohol is $\frac{3}{5}$. Let the ratio of water and alcohol in container 2 be $4:5$. This means for every 9 units of mixture, there are 4 units of water and 5 units of alcohol. The fraction of alcohol is $\frac{5}{9}$. Let $x$ be the ratio in which the two mixtures are mixed. Then the ratio of alcohol in the new mixture is given by:
$$ \frac{\frac{3}{5}x + \frac{5}{9}}{x + 1} $$
We want the ratio of alcohol to water in the new mixture to be $7:5$, which implies the fraction of alcohol in the new mixture is $\frac{7}{12}$. Therefore we set up the equation:
$$ \frac{\frac{3}{5}x + \frac{5}{9}}{x + 1} = \frac{7}{12} $$
Cross-multiplying:
$$ 12\left(\frac{3}{5}x + \frac{5}{9}\right) = 7(x + 1) $$
$$ 12\left(\frac{27x}{45} + \frac{25}{45}\right) = 7x + 7 $$
$$ 12\left(\frac{27x + 25}{45}\right) = 7x + 7 $$
$$ \frac{4(27x + 25)}{15} = 7x + 7 $$
$$ 4(27x + 25) = 15(7x + 7) $$
$$ 108x + 100 = 105x + 105 $$
$$ 3x = 5 $$
$$ x = \frac{5}{3} $$
Therefore, the ratio in which the mixtures should be mixed is $5:3$.
Q17: The diluted wine contains only 8 litres of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many litres of mixture shall be replaced with pure wine if there was initially 32 litres of water in the mixture ?
A. 4
B. 5
C. 8
D. None of these
Correct Answer: B
Solution: Initially, the mixture contains 8 liters of wine and 32 liters of water, totaling 40 liters. The wine concentration is $8/40 = 20\%$. Let $x$ liters of the mixture be replaced with pure wine. This means $x$ liters of the 20% mixture is removed, and $x$ liters of pure wine (100% wine) is added. The amount of wine removed is $0.20x$. The amount of water removed is $0.80x$. The remaining wine is $8 - 0.20x$. The remaining water is $32 - 0.80x$. After adding $x$ liters of pure wine, the new amount of wine is $(8 - 0.20x) + x = 8 + 0.80x$. The total volume remains 40 liters. The new concentration is 30%, so we have the equation:
$$ \frac{8 + 0.80x}{40} = 0.30 $$
$$ 8 + 0.80x = 12 $$
$$ 0.80x = 4 $$
$$ x = \frac{4}{0.80} $$
$$ x = 5 $$
Therefore, 5 liters of the mixture must be replaced with pure wine.
Q18: The shopkeeper mixed 40 kg refined oil with vegetable oil worth Rs. 60 per kg. Thus he gains Rs. 10 after selling the mixture of the two oils. The price of the first oil is :
A. 20
B. 25
C. 45
D. Cannot be determined
Correct Answer: D
Solution: Let the price of refined oil be $x$ Rs/kg. The shopkeeper mixed 40 kg of refined oil with vegetable oil. Let's assume $y$ kg of vegetable oil was mixed. Total cost price of the mixture = $40x + 60y$
Total quantity of the mixture = $40 + y$ kg
Let the selling price of the mixture be $S$ Rs/kg. Total selling price = $S(40+y)$
Profit = Total selling price - Total cost price = $S(40+y) - (40x + 60y) = 10$
We need more information to solve this problem. The question is incomplete; it lacks information about the selling price ($S$) or the quantity of vegetable oil ($y$) mixed. Therefore, a definitive answer cannot be calculated. The question as stated is unsolvable.
Q19: 4 kg of a metal contains 1/5 th copper and rest is zinc. Another 5 kg of metal contains 1/6th copper and rest is zinc. The ratio of copper and zinc into the mixture of these 2 metals is:
A. 49 : 221
B. 39 : 231
C. 94 : 181
D. None of these
Correct Answer: A
Solution: Step 1: Calculate the amount of copper in 4 kg of metal: $\frac{1}{5} \times 4 \text{ kg} = 0.8 \text{ kg}$ copper. The remaining amount is zinc: $4 \text{ kg} - 0.8 \text{ kg} = 3.2 \text{ kg}$ zinc. Step 2: Calculate the amount of copper in 5 kg of metal: $\frac{1}{6} \times 5 \text{ kg} = \frac{5}{6} \text{ kg}$ copper. The remaining amount is zinc: $5 \text{ kg} - \frac{5}{6} \text{ kg} = \frac{25}{6} \text{ kg}$ zinc. Step 3: Calculate the total amount of copper in the mixture: $0.8 \text{ kg} + \frac{5}{6} \text{ kg} = \frac{4.8 + 5}{6} \text{ kg} = \frac{9.8}{6} \text{ kg} = \frac{49}{30} \text{ kg}$
Step 4: Calculate the total amount of zinc in the mixture: $3.2 \text{ kg} + \frac{25}{6} \text{ kg} = \frac{19.2 + 25}{6} \text{ kg} = \frac{44.2}{6} \text{ kg} = \frac{221}{30} \text{ kg}$
Step 5: Calculate the ratio of copper to zinc in the mixture: $\frac{49}{30} : \frac{221}{30} = 49 : 221$
Q20: 450 litres of a mixture of milk and water contain the milk and water in the ratio 9 :1. How much water should be added to get a new mixture containing milkand water in the ratio 3:1?
A. 54
B. 90
C. 45
D. 63
Correct Answer: B
Solution: Let the quantity of milk in the mixture be $9x$ liters and the quantity of water be $x$ liters. Total quantity = $9x + x = 10x = 450$ liters
Therefore, $x = 45$ liters. Quantity of milk = $9x = 9 \times 45 = 405$ liters
Quantity of water = $x = 45$ liters
Let $y$ liters of water be added to the mixture. The new ratio of milk to water is 3:1. The quantity of milk remains the same (405 liters). The quantity of water becomes $45 + y$ liters. The ratio is given by:
$$ \frac{405}{45 + y} = \frac{3}{1} $$
$$ 405 = 3(45 + y) $$
$$ 405 = 135 + 3y $$
$$ 3y = 405 - 135 $$
$$ 3y = 270 $$
$$ y = \frac{270}{3} $$
$$ y = 90 \text{ liters} $$
Therefore, 90 liters of water should be added.
Q21: The ratio of petrol and kerosene in the container is 3: 2 when 10 litres of the mixture is taken out and is replaced by the kerosene, the ratio becomes 2: 3. The total quantity of the mixture in the container is :
A. 25
B. 30
C. 45
D. Cannot be determined
Correct Answer: B
Solution: Let the quantity of petrol be $3x$ and kerosene be $2x$. Total quantity = $5x$
When 10 liters of mixture is taken out, the amount of petrol removed is $\frac{3}{5} \times 10 = 6$ liters and kerosene removed is $\frac{2}{5} \times 10 = 4$ liters. Remaining petrol = $3x - 6$
Remaining kerosene = $2x - 4$
10 liters of kerosene is added. New quantity of kerosene = $2x - 4 + 10 = 2x + 6$
New ratio of petrol to kerosene = $\frac{3x - 6}{2x + 6} = \frac{2}{3}$
Cross-multiplying: $3(3x - 6) = 2(2x + 6)$
$9x - 18 = 4x + 12$
$5x = 30$
$x = 6$
Total quantity = $5x = 5 \times 6 = 30$ liters
Q22: From a container, 6 litres milk was drawn out and was replaced by water. Again 6 litres of mixture was drawn out & was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9 : 16. The quantity of mixture is :
A. 15
B. 16
C. 25
D. 31
Correct Answer: A
Solution: Let the initial quantity of milk in the container be $x$ litres. After the first operation, the quantity of milk remaining is $x - 6$ litres. The total quantity remains $x$ litres. The fraction of milk remaining is $\frac{x-6}{x}$. After the second operation, 6 litres of the mixture is drawn out. The amount of milk drawn out is $6 \times \frac{x-6}{x} = \frac{6(x-6)}{x}$ litres. The amount of milk remaining after the second operation is $(x-6) - \frac{6(x-6)}{x} = (x-6)(1 - \frac{6}{x}) = (x-6)\frac{(x-6)}{x} = \frac{(x-6)^2}{x}$ litres. The ratio of milk to water after two operations is 9:16. The total quantity is still $x$ litres. Therefore, the amount of milk is $\frac{9x}{9+16} = \frac{9x}{25}$ litres. Equating the amount of milk remaining after two operations:
$$ \frac{(x-6)^2}{x} = \frac{9x}{25} $$
$$ 25(x-6)^2 = 9x^2 $$
$$ 25(x^2 - 12x + 36) = 9x^2 $$
$$ 25x^2 - 300x + 900 = 9x^2 $$
$$ 16x^2 - 300x + 900 = 0 $$
Dividing by 4:
$$ 4x^2 - 75x + 225 = 0 $$
This is a quadratic equation. We can solve it using the quadratic formula or factorization. Factorization yields:
$$ (x-15)(4x-15) = 0 $$
Therefore, $x = 15$ or $x = \frac{15}{4}$. Since the initial quantity must be greater than 12 (to allow for two 6-litre extractions), $x = 15$ litres. The quantity of the mixture is $x = 15$ litres.
