Daily Inshorts - 01 July 2025

Daily Inshorts - 01 July 2025

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Government wins welfare bill vote after big concessions to rebels

MPs approved the Universal Credit and Personal Independence Payment Bill but only after ministers made big changes.

Who are the welfare bill rebels? Find out how your MP voted

Check whether your MP voted for or against the Universal Credit and Personal Independence Payment Bill

Israel has agreed to conditions for 60-day Gaza ceasefire, Trump says

US president warns Hamas "it will only get worse" if they do not accept the deal.

Diddy jury to keep deliberating after deadlocking on most serious charge

The panel reached a verdict on four of the five counts, but could not agree on the most racketeering count.

Three former bosses of Lucy Letby arrested on suspicion of gross negligence manslaughter

All three worked at the Countess of Chester Hospital when the nurse killed babies at its neonatal unit.

Scheduled Castes survey extended only in Bengaluru till July 6

IIMK, Tata Power to collaborate in training professionals in power sector

Minister seeks report on the deaths of tigers in the last five-and-a-half years in Karnataka

Akhilesh, the Ambedkarite

He has emerged as a counterpoint to Hindutva forces

Health Commissioner for probe into allegations of unfair clinical trials

Daily Inshorts - 30 June 2025

Daily Inshorts - 30 June 2025

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Labour MPs press Kendall on rollout of benefit changes

The government was forced into concessions on its welfare plan following a backlash among its own MPs.

Police launch criminal investigation into Bob Vylan and Kneecap Glastonbury sets

It follows performances from both bands on Saturday at the Glastonbury music festival in Somerset.

Israeli strike on Gaza seafront cafe kills at least 20 Palestinians, witnesses and rescuers say

The outdoor cafe was frequently used by journalists, activists and local residents.

Is RFK Jr's divisive plan to Make America Healthy Again fearmongering - or revolutionary?

The most powerful public health official in the US is reviled by some medics - but even some of his critics accept that he is bringing drive to healthcare areas that have long been neglected

Heatwave peak sees parts of UK climb to 33C

The rise in temperature coincides with the beginning of Wimbledon and the end of the Glastonbury festival.

WaveX invites startups to develop AI-powered real-time multilingual translation solution

The registrations for the challenge will be open from June 30 to July 22

Police resort lathi-charge in Bhogandih on the occasion of Hul Diwas

Jharkhand Bharatiya Janata Party (BJP) president and Leader of opposition Babulal Marandi strongly condemned the incident calling it a barbaric act on the tribal community.

HC reiterates need for dedicated authority to protect Periyar

Janaki, Zumba, and everything in between

Fundamentalist voices from various religious groups are getting louder

Bihar BJP attempts to break RJD’s Muslim votes through Pasmanda

State president Dilip Jaiswal said that in Bihar, politics has always been done in the name of Muslims, but no real efforts were ever made to uplift the Pasmanda Muslims. He also assured their political representation.

Daily Inshorts - 29 June 2025

Daily Inshorts - 29 June 2025

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Keir Starmer criticises 'appalling' Bob Vylan IDF chants

The prime minister describes the punk duo's Glastonbury chants calling for death to Israel's military as "hate speech".

US must rule out more strikes before new talks, Iranian minister tells BBC

Majid Takht-Ravanchi said the Trump administration has "not made their position clear" on further attacks.

'Mariupol is diseased': Residents deny Russia's stories about occupied city

Russian shattered Mariupol with a months-long siege in 2022. Now, it says it's rebuilding it.

Boeing's 787 Dreamliner was deemed the 'safest' of planes. The whistleblowers were always less sure

Long before the Air India tragedy, the cause of which is still to be determined, people who had worked on the 787 had raised concerns about the production standards

Israel orders evacuations in northern Gaza as Trump pushes for ceasefire

At least 86 people were killed as the result of Israeli attacks in the 24 hours before midday Sunday, the Hamas-run health ministry said.

24-year-old Indian woman who went to U.S. for arranged marriage goes missing

Simran arrived on a flight from India on June 20. Surveillance footage shows the woman looking at her phone and seemingly waiting for someone, police said.

Murder accused highway robber killed in police encounter in UP's Baghpat

Sandeep, a resident of Haryana's Rohtak, was wounded in the encounter and later succumbed to his injuries, police said.

No meat, eggs or school uniforms in State Gurukuls

Contractors and suppliers of these essentials are vexed as their payments are pending for several months

Golconda fort turns into sea of devotion, tradition for Bonalu

Bonams, or earthen pots containing cooked rice, jaggery, curd and other offerings balanced on the heads of women, formed a striking sight against the backdrop of the ancient fort

Compulsory injunction orders set to make secret child marriages difficult in Banswara

Daily Inshorts - 28 June 2025

Daily Inshorts - 28 June 2025

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Starmer says fixing welfare is a 'moral imperative'

The prime minister described the benefits system as "broken" a day after he was forced to U-turn on plans for reforms.

Southern Europe swelters as heatwave spreads

Spain, Italy and France are among the countries issuing warnings to protect health and stop wildfires.

Child, 7, dies after tree falls in park

Police say another child, aged six, is in a serious condition.

Venice divided as lavish Bezos wedding brings glamour and protests

Venetians have mixed feelings over the Amazon founder's lavish three-day party in their city.

Budapest Pride draws huge crowds in defiance of Orban legal threats

Tens of thousands have gathered for the LGBTQ march in Hungary's capital, despite a police ban and warning from PM Viktor Orban.

Keeladi | Excavating the past

Findings at the excavation site in Sivaganga district offer compelling evidence that urban civilisation existed in Tamil Nadu during the Sangam age

Where does India lag in gender metrics? | Explained

What is India’s standing in the World Economic Forum’s Global Gender Gap Index for 2025?

Consumer panel slaps textile dealer with fine of ₹36,500 for selling defective sari

BJP bringing up Katchatheevu issue to divert attention from Centre’s failure to secure T.N. fishermen’s rights: TNCC chief

Refuting External Affairs Minister S. Jaishankar’s statement, he clarifies that Katchatheevu was ceded to Sri Lanka during Emergency

What are the issues around deportation? | Explained

Why is there a distinction to be made between people who are being deported and those who are being pushed back? What are the different laws that deal with immigration and foreigners in India? What is the situation on the ground in border States such as Assam and West Bengal?

Daily Inshorts - 27 June 2025

Daily Inshorts - 27 June 2025

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Supreme Court curbs judges' power to block Trump's orders in birthright citizenship case

Because of the ruling to limit injunctions, Trump's birthright citizenship order will be able to take effect, 30 days after the courts opinion was filed, the court said.

We've got the right balance, says PM after benefits U-turn

The prime minister has made concessions on his welfare bill after an angry response from 120 of his own MPs.

Backbenchers left feeling bruised after benefit cuts row

After the PM's efforts to mend relations with many on Labour's left, plenty are still unhappy.

Health alerts come into force ahead of second heatwave

The UK could see its hottest day of the year on Monday, as a likely heatwave coincides with Glastonbury and Wimbledon.

Anna Wintour's legacy and who might replace her as Vogue editor

Dame Anna announced this week she was stepping down as editor-in-chief after 37 years.

Operation Sindhu: Fear, flight, and an uncertain future

Soon after the most recent conflict in West Asia broke out, the Indian government evacuated more than 1,400 Indian nationals from Iran and more than 1,100 from Israel under Operation Sindhu. Many of them are medical students

Adani indictment case: U.S. SEC updates court on efforts to serve legal documents

U.S. SEC has to serve the summons to Gautam Adani and his nephew Sagar through proper diplomatic channels, as it has no jurisdiction to summon a foreign national directly; Court asks for update by August 11

Diesel disaster: 19 vehicles break down before M.P CM’s visit

Pink buses offer safe ride to women in Bihar

The special pink bus services in Bihar, run on CNG, are dedicated to women, and the responsibility of operating them has also been given to women, including conductor and nodal officers in each division

Gurugram Police to hit brakes on road stunts

Daily Inshorts - 26 June 2025

Daily Inshorts - 26 June 2025

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Starmer set to announce welfare climbdown in deal with Labour rebels

Cuts to some disability benefits will only hit future claimants, not those already on it, it is understood.

Misogyny is an epidemic fuelled by social media, Amy Hunt tells BBC in first interview

People “should be very concerned” about sexist, hateful content on social media, says Amy, whose mother and two sisters were murdered last year.

Child Q unsure she will 'feel normal again' after police strip-search

The woman, who was 15 at the time of the strip-search, was wrongly suspected of possessing cannabis.

Iran leader says US gained nothing from strikes as Hegseth hails 'historic success'

The ayatollah speaks for the first time since the conflict ended, as the US insists Iran's nuclear sites are destroyed.

How is your hospital doing as NHS battles to bring down waiting times?

Use our interactive tracker to see if treatment waits are getting better at your local hospital

Mahim Juma Masjid Trust launch Online Azan app amid loudspeaker row

The Online Azan app gets the Masjid registered, and people associated with the particular masjid can be selected and listened to

Trinamool Congress on the defensive over ‘involvement’ in kangaroo courts

TMC Minister Udayan Guha tried to distance himself and party workers from the public justice system; BJP leaders called it a pre-election ploy

U.S. requires visa applicants to share social media used in 5 years: U.S. Embassy in India

The embassy has stressed that visa applicants are required to provide social media identifiers. All available information will be used for visa screening and vetting

TMC issues notice to party MLA for offering money to parents of child killed in bomb attack

The whole incident of Debra MLA Humayun Kabir offering money to the family on June 25 was caught on camera, where the mother of the child Sabina Khatun gets angry and says they ‘do not want any money’

Decision on India’s 2036 Olympic Games bid set to take longer than expected

International Olympic Committee President Kirsty Coventry announces pause in 2036 Olympics bid decision and sets up working group for future host selection

Daily Inshorts - 25 June 2025

Daily Inshorts - 25 June 2025

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A political storm is brewing over welfare cuts - can Starmer ride it out?

Conversations are continuing at the heart of government on the least worst course of action in the face of a significant backbench rebellion.

What are the government's planned welfare cuts and how much will they save?

Labour MPs have threatened to vote against the government's welfare reform proposals.

When Iran's Supreme Leader emerges from hiding he will find a very different nation

The war has left the country significantly weakened - and left Ayatollah Ali Khamenei a diminished leader

Damaged or destroyed - how much does leaked US report on Iran's nuclear sites tell us?

Fordo is probably the most spied-on place on the planet - and work to understand what is happening there is set to intensify further.

Five takeaways from Nato's big summit on hiking defence spending

There were unexpected moments of levity among the momentous decisions on raising spending to levels not seen since the Cold War.

Chemotherapy drugs made by Indian firms fail quality tests, shows study

A landmark study published on June 26 has reported that about a fifth of cancer drugs tested failed quality tests; 16 of the 17 implicated manufacturers are India-based

CBI arrests three people in fake postage stamps scam worth ₹2.5 crore

The three arrested individuals are Pappu Singh, Rajesh Kumar and Mahendra Kumar

Bombay High Court questions legal basis of stipend for junior lawyers

The High Court was hearing a petition filed by 12 junior advocates seeking a ₹5,000 monthly stipend during the first three years of legal practice

Himachal Pradesh cloudbursts, flash floods | 2 dead, 20 feared swept away in Kangra, heavy rain continues

Tragic cloudbursts and flash floods in Himachal Pradesh cause casualties and destruction, with rescue operations underway

Shiv Sena (UBT) defends Emergency, calls it ‘constitutionally valid’

Sena (UBT) MP Sanjay Raut statement comes after Prime Minister Narendra Modi called the Emergency Samvidhan Hatya Diwas

Daily Inshorts - 24 June 2025

Daily Inshorts - 24 June 2025

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UK to purchase nuclear-carrying fighter jets

Downing Street says the move is "the biggest strengthening of the UK's nuclear posture in a generation".

Keir Starmer vows to press on with welfare cuts as rebellion grows

More than 120 Labour MPs are backing plans to block cuts to disability and sickness-related benefits.

Russian naval ship 'disguised' itself while passing through English Channel

The Boikiy emitted a fake ID signal while sailing through the waterway alongside two sanctioned oil tankers.

This burger was made in a lab from cow cells… Should it really be served in restaurants?

Lab-grown beef, chicken and even quail are served in restaurants in some countries around the world - and now some cultivated meats could soon be sold in the UK too

'A slap in the face' - Asos bans shoppers for making too many returns

The retailer has been cracking down on customers with high return rates - but some say it is unfair.

Modi Government left no stone unturned in ruining country’s rapidly growing economy: Congress

Congress criticises Modi government for lowest savings account interest rates in 25 years, accusing them of “ruining the economy”

Pahalgam attackers not locals; probably got shelter by ‘coercion’: CM Omar Abdullah

The people who shot and killed those 26 persons were all outsiders, says the Chief Minister

Minor killed in Kaliganj bomb blast, 4 arrested in West Bengal

In a report to the West Bengal Chief Electoral Officer, the police admitted that crude bombs were hurled from celebratory processions which killed the girl

Uttar Pradesh BJP faces heat over allegation that ‘MLA struck official’

Banda MLA Prakash Dwivedi admitted scolding the officer for alleged misconduct; This is the second incident in less than a week in which a BJP MLA has been accused of misconduct in the State

Dhubri communal tensions: Assam CM says main accused identified; urges surrender

CM Himanta Biswa Sarma assesses law and order situation and declares a beef-free buffer zone around a major Sikh temple in the western Assam town

Daily News - 23 June 2025

Daily News - 23 June 2025

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What is the Strait of Hormuz and why does it matter?

Iran's threat to block the world's most vital oil transit point has raised fears of major global economic consequences.

Watch: How successful have the US strikes on Iran been?

BBC security analyst Gordon Corera examines how much damage is likely to have been caused to Iran's nuclear sites.

Decoy flights and seven B-2 stealth bombers - how US says it hit Iran's nuclear sites

A timeline of how the complex mission unfolded was laid out in a Pentagon briefing.

Return to the negotiating table, David Lammy urges Iran

Iran has said there will be "everlasting consequences" to three US strikes at the weekend.

Palestine Action to be banned, home secretary confirms

The announcement comes as the group holds a protest in central London.

Focus is on skill development and job creation, says Dinakar

Andhra Pradesh government is working for creating 20 lakh jobs in five years, says 20-Point Programme Chairperson

APSSDC to hold mega job melas at Madakasira, Madanapalle on June 26, 27

Minister Ponnam Prabhakar questions Kavitha’s credibility on BC issues

‘Farm fests’ to be held at Kerala Agriculture department farms

Farm produce unique to each farm and seed materials will be on display and sale; part of bid to popularise farming among people

Ranjitha’s body identified through DNA test

The DNA sample matched with that of her mother. The sample from her brother did not yield a match and hence samples were taken from her mother and children

Daily Inshorts - 23 June 2025

Daily Inshorts - 23 June 2025

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Talk of regime change resonates with Iranians fleeing across border

A steady stream of Iranians are crossing into Armenia by foot, laden with luggage and pets.

Did Trump have the legal authority to strike Iran?

Some lawmakers have called Trump's strikes on Iran "unconstitutional" - so did he have the authority to order them?

What we know about Iran's attack on US base in Qatar

The Iranian military confirms it launched missiles in retaliation for American strikes against its nuclear sites.

Israel says it struck Tehran's Evin prison and Fordo access routes

Iran's judiciary says the attack damaged parts of Evin, a notorious facility which holds many political prisoners.

What is the Strait of Hormuz and why does it matter?

Iran's threat to block the world's most vital oil transit point has raised fears of major global economic consequences.

Deadline for exercising option under Unified Pension Scheme extended

The Finance Ministry extends UPS option exercise deadline to September 30, 2025 for government employees under National Pension System

‘Beej Utsav’ highlights role of indigenous seeds in agricultural sustainability

Held in the tribal belt at the tri-junction of Rajasthan, Madhya Pradesh, and Gujarat, participants at the ‘seed festival’ were apprised of the significance of seed heritage, biodiversity, and climate consciousness

India slams OIC for ‘incorrect’ remarks that reflect ‘Pakistan’s influence’

The MEA said the OIC's repeated failure to acknowledge the documented threat of terrorism emanating from Pakistan reflects a wilful disregard for facts

DRDO offers 28 indigenous weapon systems to defence forces for emergency procurement

Under this clause, the three forces can replenish stock as per their requirement

Two J&K residents held for displaying U.S., Israel flags

A police spokesman said the two individuals were detained for installing foreign flags during night hours in an apparent attempt “to disturb public peace and order”

Daily Inshorts - 22 June 2025

Daily Inshorts - 22 June 2025

All fresh Inshorts-style stories for today.

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Daily Inshorts - 22 June 2025

Daily Inshorts - 22 June 2025

All fresh Inshorts-style stories for today.

No fresh news fetched today due to API issue. Please check later.

Daily Quant Practice - 2CRQ - Single Post with Toggle Answer

Q1: Raja divided 35 sweets among his daughters Rani and Sita in the ratio 4: 3. How many sweets did Rani get?

Correct Option:

Correct Answer: 20

Explanation:
The total parts in the ratio are $4+3=7$. The value of one part is $35 \div 7 = 5$ sweets. Rani's share is 4 parts, so she gets $4 \times 5 = 20$ sweets.

Q2: If p:Q=3:4, find 5P: 7Q.

1. $\frac{20}{37}$
2. $\frac{3}{4}$
3. $\frac{15}{28}$
4. $\frac{20}{37}$

Correct Option: C

Correct Answer: 15/28

Explanation:
We are given $\frac{P}{Q} = \frac{3}{4}$. We need to find $\frac{5P}{7Q}$. This can be written as $\frac{5}{7} \times \frac{P}{Q}$. Substituting the given ratio: $\frac{5}{7} \times \frac{3}{4} = \frac{15}{28}$.

Q3: Ratio of two numbers is 3:5 and their sum is 40. Find the smaller of the two numbers.

Correct Option:

Correct Answer: 15

Explanation:
Let the numbers be 3x and 5x. Their sum is $3x + 5x = 40 \implies 8x=40 \implies x=5$. The numbers are $3(5)=15$ and $5(5)=25$
The smaller number is 15.

Q4: If a:b=7:3, find a+b:a-b.

1. 05:02:00
2. 02:05:00
3. 07:03:00
4. 03:07:00

Correct Option: A

Correct Answer: 05:02:00

Explanation:
Let a = 7k and b = 3k. $a+b = 7k+3k = 10k$ $a-b = 7k-3k = 4k$ The ratio $(a+b):(a-b) is $10k:4k$, which simplifies to 5:2.

Q5: If a+b : a-b = 3:2, find a : b.

1. 05:01:00
2. 01:05:00
3. 03:05:00
4. 05:03:00

Correct Option: A

Correct Answer: 05:01:00

Explanation:
We are given $\frac{a+b}{a-b} = \frac{3}{2}$. Cross-multiply: $2(a+b) = 3(a-b) \implies 2a+2b = 3a-3b$. Rearranging the terms gives $5b=a$, so $\frac{a}{b} = \frac{5}{1}$
The ratio is 5:1.

Q6: If $\frac{x+y}{2x+y}=\frac{4}{5}$ then find $\frac{2x+y}{3x+y}$.

1. $\frac{4}{5}$
2. $\frac{5}{6}$
3. $\frac{6}{7}$
4. $\frac{3}{4}$

Correct Option: B

Correct Answer: $\frac{5}{6}$

Explanation:
From the given equation, cross-multiply: $5(x+y) = 4(2x+y) \implies 5x+5y = 8x+4y \implies y=3x$. Now substitute y=3x into the expression to be found: $\frac{2x+(3x)}{3x+(3x)} = \frac{5x}{6x} = \frac{5}{6}$.

Q7: If x+y+z = 120 and $x = \frac{1}{2}y$ and $y = \frac{2}{3}z$. find z.

Correct Option:

Correct Answer: 60

Explanation:
Express x and y in terms of z. $y = \frac{2}{3}z$ $x = \frac{1}{2}y = \frac{1}{2}(\frac{2}{3}z) = \frac{1}{3}z$ Substitute into the sum: $\frac{1}{3}z + \frac{2}{3}z + z = 120 \implies z+z=120 \implies 2z=120 \implies z=60$.

Q8: If a:b=4:1, find $\frac{a-3b}{2a-b^{2}}$.

1. $\frac{2}{7}$
2. $\frac{1}{7}$
3. $\frac{3}{7}$
4. Cannot be determined

Correct Option: D

Correct Answer: Cannot be determined

Explanation:
Let a = 4k and b = k. The expression becomes $\frac{4k-3k}{2(4k)-k^2} = \frac{k}{8k-k^2} = \frac{k}{k(8-k)} = \frac{1}{8-k}$. Since the value of the expression depends on k, which is unknown, the answer cannot be determined.

Q9: (a) Duplicate ratio of 3: 4. (b) Triplicate ratio of 2: 3. (c) Sub-duplicate ratio of 16:9. (d) Mean proportional of 16 and 4.

1. (a)D (b)C (c)B (d)C
2. (a)D (b)C (c)B (d)C
3. (a)D (b)C (c)B (d)C
4. (a)D (b)C (c)B (d)C

Correct Option: D, C, B, C

Correct Answer: (a) 9:16 (b) 8:27 (c) 4:3 (d) 8

Explanation:
The options provided seem to be placeholders
The correct answers are: (a) Duplicate (squaring): $3^2:4^2 \implies 9:16$ (b) Triplicate (cubing): $2^3:3^3 \implies 8:27$ (c) Sub-duplicate (square root): $\sqrt{16}:\sqrt{9} \implies 4:3$ (d) Mean proportional: $\sqrt{16 \times 4} = \sqrt{64} = 8$

Q10: Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second numbers added to the difference of the third and the second numbers is 21.

1. 12, 8, 16
2. 6, 4, 8
3. 9, 6, 24
4. 9, 6, 12

Correct Option: D

Correct Answer: 9, 6, 12

Explanation:
Let the numbers be 3x, 2x, 4x. The condition is $(3x+2x) + (4x-2x) = 21$. $5x + 2x = 21 \implies 7x=21 \implies x=3$. The numbers are $3(3)=9$, $2(3)=6$, and $4(3)=12$.

Q11: In a class of 30 students, which of the following can't be the ratio of boys and girls?

1. 02:03:00
2. 01:05:00
3. 04:05:00
4. 02:01:00

Correct Option: C

Correct Answer: 04:05:00

Explanation:
For a ratio to be possible, the sum of its parts must be a factor of the total number of students (30). • 2:3 -> Sum=5
30 is divisible by 5
(Possible) • 1:5 -> Sum=6
30 is divisible by 6
(Possible) • 4:5 -> Sum=9
30 is not divisible by 9
(Not possible) • 2:1 -> Sum=3
30 is divisible by 3
(Possible)

Q12: If a: b=2:3 and b:c=5:7 then find a: b: c.

1. 10:15:21
2. 10:21:15
3. 09:12:14
4. 12:07:18

Correct Option: A

Correct Answer: 10:15:21

Explanation:
To combine the ratios, the value for the common term b must be the same
The LCM of the b values (3 and 5) is 15. • a:b = 2:3 (multiply by 5) \implies 10:15 • b:c = 5:7 (multiply by 3) \implies 15:21 Combining them gives a:b:c = 10:15:21.

Q13: At a party, there are a total of 28 adults. If x ladies join the party, the ratio of the number of ladies to that of gents will change from 3: 4 to 5: 4. Find x.

Correct Option:

Correct Answer: 8

Explanation:
Initially, there are 28 adults in the ratio 3:4 (L:G). Number of Gents = $\frac{4}{7} \times 28 = 16$. Number of Ladies = $\frac{3}{7} \times 28 = 12$. After x ladies join, the new number of ladies is 12+x
The number of gents remains 16
The new ratio is 5:4. $\frac{12+x}{16} = \frac{5}{4} \implies 4(12+x) = 80 \implies 48+4x=80 \implies 4x=32 \implies x=8$.

Q14: The monthly salaries of X and Y are in the ratio 3:4. The monthly expenditures of X and Y are in the ratio 4: 5. Find the ratio of the monthly savings of X and Y.

1. 05:03:00
2. 04:07:00
3. 03:05:00
4. Cannot be determined

Correct Option: D

Correct Answer: Cannot be determined

Explanation:
Let salaries be 3k and 4k
Let expenditures be 4m and 5m. Saving = Salary - Expenditure. Savings ratio = $(3k-4m) : (4k-5m)$. Since there is no information to relate the constants k and m, the ratio cannot be simplified to a numerical value.

Q15: The present ages of Rohit and Sunil are in the ratio 3:5. 10 years hence, the ratio of their ages will be 4: 5. Find the present age of Rohit. (in years)

Correct Option:

Correct Answer: 6

Explanation:
Let the present ages be 3x and 5x. In 10 years, their ages will be 3x+10 and 5x+10. The new ratio is $\frac{3x+10}{5x+10} = \frac{4}{5}$. Cross-multiply: $5(3x+10) = 4(5x+10) \implies 15x+50 = 20x+40 \implies 10=5x \implies x=2$. Rohit's present age is $3x = 3(2) = 6$ years.

Q16: x varies directly as the square of y. When $y=8$, $x=192$. Find x when $y=10$.

1. 100
2. 30
3. 300
4. 200

Correct Option: C

Correct Answer: 300

Explanation:
The relation is $x = ky^2$. First, find the constant k: $192 = k(8^2) \implies 192 = 64k \implies k=3$. The formula is $x = 3y^2$. When $y=10$, $x = 3(10^2) = 3(100) = 300$.

Q17: Quantities a and b are inversely proportional to each other. When a=8, b=240. Find b when a=6.

Correct Option:

Correct Answer: 320

Explanation:
The relation is ab = k (a constant). First, find k: $k = 8 \times 240 = 1920$. The formula is ab = 1920. When a=6, $6 \times b = 1920 \implies b = 1920 / 6 = 320$.

Q18: Quantity A varies directly with the sum of the quantities B and C. If B increases by 2 and C increases by 4, by how much does A increase?

1. 2
2. 4
3. 6
4. Cannot be determined

Correct Option: D

Correct Answer: Cannot be determined

Explanation:
The relation is $A = k(B+C)$. Let the initial state be $A_1 = k(B_1+C_1)$. The new state is $A_2 = k((B_1+2)+(C_1+4)) = k(B_1+C_1+6) = k(B_1+C_1) + 6k$. The increase is $A_2 - A_1 = 6k$
Since the constant of proportionality k is unknown, the increase cannot be determined.

Q19: Quantity P varies inversely with the product of Q and R. When Q=6 and R=12, P=75. Find P when Q=5 and R=10.

Correct Option:

Correct Answer: 108

Explanation:
The relation is $PQR = k$ (a constant). First, find k: $k = 75 \times 6 \times 12 = 5400$. The formula is $PQR = 5400$. When Q=5 and R=10, $P \times 5 \times 10 = 5400 \implies 50P = 5400 \implies P = 108$.

Q20: A varies directly with B when C is constant and inversely with C when B is constant. A is 16, when B is 28 and C is 7. Find the value of A, when B is 9 and C is 6.

1. 6
2. 7
3. 8
4. 9

Correct Option: A

Correct Answer: 6

Explanation:
This is joint variation: $A = k\frac{B}{C}$. First, find k: $16 = k \frac{28}{7} \implies 16 = 4k \implies k=4$. The formula is $A = \frac{4B}{C}$. When B=9 and C=6, $A = \frac{4 \times 9}{6} = \frac{36}{6} = 6$.

Daily Quant Practice - 1B - Single Post with Toggle Answer

Q1: Solve: $\frac{x}{2}+2y=14$ $3x+\frac{y}{6}=13.$

1. $x=2, y=6$
2. $x=4, y=6$
3. $x=4, y=12$
4. $x=2, y=12$

Correct Option: B

Correct Answer: x=4, y=6

Explanation:
1: Multiply the first equation by 2 to get $x + 4y = 28$.
2: Multiply the second equation by 6 to get $18x + y = 78$.
3: From the second new equation, $y = 78 - 18x$.
4: Substitute this into the first new equation: $x + 4(78 - 18x) = 28$.
5: $x + 312 - 72x = 28 \implies -71x = -284 \implies x=4$.
6: Substitute x=4 to find y: $y = 78 - 18(4) = 78 - 72 = 6$.

Q2: Solve: $3(x+5)+7(y-2)=-5,$ $2(x+6)-\frac{4-y}{5}=5.$

1. $x=2, y=-1$
2. $x=-2, y=1$
3. $x=-3, y=-1$
4. None of these

Correct Option: C

Correct Answer: None of these

Explanation:
1: Simplify the first equation: $3x+15+7y-14=-5 \implies 3x+7y=-6$.
2: Simplify the second equation: $2x+12 - \frac{4-y}{5}=5 \implies 2x+7 = \frac{4-y}{5} \implies 10x+35 = 4-y \implies 10x+y=-31$.
3: None of the given options satisfy both simplified equations
For example, testing x=-2, y=1 in the first equation gives $3(-2)+7(1) = 1$, which is not -6.

Q3: Solve: $\frac{x}{4}+2y=7:\frac{19}{x+(y/4)}=4.$

1. $x=2, y=3$
2. $x=-2, y=6$
3. $x=4, y=3$
4. $x=-4, y=6$

Correct Option: C

Correct Answer: x=4, y=3

Explanation:
1: Simplify the first equation: $x + 8y = 28$.
2: Simplify the second equation: $19 = 4(x + y/4) \implies 19 = 4x + y$.
3: From the second simplified equation, $y = 19 - 4x$.
4: Substitute this into the first: $x + 8(19 - 4x) = 28 \implies x + 152 - 32x = 28 \implies -31x = -124 \implies x=4$.
5: Find y: $y = 19 - 4(4) = 3$.

Q4: The number of pencils with P is $5/3$ times the number of pencils with Q. If P has 18 pencils more than Q, then find the total number of pencils with them.

Correct Option:

Correct Answer: 72

Explanation:
Let the number of pencils be P and Q
1
$P = \frac{5}{3}Q$ 2
$P = Q + 18$ Substitute P: $\frac{5}{3}Q = Q + 18 \implies \frac{2}{3}Q = 18 \implies Q=27$. Then, $P = 27 + 18 = 45$. Total pencils = $P+Q = 45+27 = 72$.

Q5: A question paper consists of 50 questions. Each correct answer fetches three marks and one mark is deducted for each wrong answer. A student who attempted all the questions scored 90 marks. Find the number of questions answered correctly by him.

Correct Option:

Correct Answer: 35

Explanation:
Let c be the number of correct answers and w be the number of wrong answers
1
$c + w = 50$ 2
$3c - w = 90$ Add the two equations: $4c = 140 \implies c = 35$.

Q6: The sum of the ages of two friends A and B 18 years ago was half of the sum of their ages today. Presently, A is twice as old as B. What is the present age of A (in years)?

Correct Option:

Correct Answer: 48

Explanation:
Let the present ages be A and B
1
$(A-18) + (B-18) = \frac{1}{2}(A+B) \implies A+B-36 = \frac{A+B}{2} \implies 2A+2B-72=A+B \implies A+B=72$
2
$A=2B$
Substitute A: $2B+B = 72 \implies 3B = 72 \implies B=24$. Present age of A is $2 \times 24 = 48 years.

Q7: A student was asked to find $3/7^{th}$ of a number and he instead multiplied it by $7/3$. As a result, he got an answer, which was more than the correct answer by 1680. What was the number?

1. 882
2. 273
3. 840
4. 1684

Correct Option: A

Correct Answer: 882

Explanation:
Let the number be N
The difference is $(\frac{7}{3}N) - (\frac{3}{7}N) = 1680$. $(\frac{49-9}{21})N = 1680 \implies \frac{40}{21}N = 1680$. $N = 1680 \times \frac{21}{40} = 42 \times 21 = 882$.

Q8: A boy has a total of ₹14 in denominations of 25 paise and 20 paise coins. If the numbers of coins of the two denominations were swapped, the total value of coins would be ₹1 less. Find the total number of coins.

Correct Option:

Correct Answer: 60

Explanation:
Let q be the number of 25p coins and t be the number of 20p coins
Value is in paise
1
$25q + 20t = 1400 \implies 5q + 4t = 280$ 2
$20q + 25t = 1300 \implies 4q + 5t = 260$ Add the two simplified equations: $9q + 9t = 540$. Divide by 9: $q + t = 60$
The total number of coins is 60.

Q9: Govind is four times as old as Ganesh is. 20 years hence, Govind's age will be twice that of Ganesh's age. Find Ganesh's present age. (in years)

1. 20
2. 10
3. 15
4. 30

Correct Option: B

Correct Answer: 10

Explanation:
Let Govind's age be Go and Ganesh's be Ga
1
$Go = 4Ga$ 2
$Go+20 = 2(Ga+20)$ Substitute Go: $4Ga+20 = 2Ga+40 \implies 2Ga = 20 \implies Ga=10$.

Q10: Five years ago, Alok's age was five times Bharan's age. Five years hence, Alok's age will be thrice that of Bharan's age. Find Bharan's present age. (in years)

Correct Option:

Correct Answer: 15

Explanation:
Let present ages be A and B
1
$A-5 = 5(B-5) \implies A-5B = -20$ 2
$A+5 = 3(B+5) \implies A-3B = 10$ Subtract the first equation from the second: $2B = 30 \implies B=15$.

Q11: Praveen's present age is twice that of Mahesh's age four years ago. Eight years hence, Praveen would be twice as old as Mahesh is today. Find the sum of their present ages.

1. 36 years
2. 44 years
3. 64 years
4. Cannot be determined

Correct Option: D

Correct Answer: Cannot be determined

Explanation:
Let present ages be P and M
1
$P = 2(M-4) \implies P = 2M-8$ 2
$P+8 = 2M$ Substituting P from the first equation into the second gives $(2M-8)+8 = 2M \implies 2M = 2M$
This is an identity, meaning the equations are dependent and there is no unique solution.

Q12: Alok's age is $5/3$ times of Alakhnanda's age. Alakhnanda is now 3 times as old as she was, when Alok was as old as Alakhnanda is today. Find Alok's age when Alakhnanda was half as old as Alok is now.

1. 60
2. 50
3. 40
4. Data insufficient

Correct Option: D

Correct Answer: Data insufficient

Explanation:
Let present ages be A and N
1
$A = \frac{5}{3}N \implies 3A = 5N$ 2
The time when Alok was N years old was A-N years ago
At that time, Alakhnanda's age was N-(A-N) = 2N-A
The condition is $N = 3(2N-A) \implies N = 6N-3A \implies 3A=5N$
Both conditions give the same relationship, so individual ages cannot be determined.

Q13: The sum of the ages of Ajay and Bala, 20 years ago was five-ninth the sum of their present ages. Ajay's present age exceeds that of Bala by 20 years. Find the present age of Ajay. (in years)

Correct Option:

Correct Answer: 55

Explanation:
Let present ages be J and B
Let the present sum be S = J+B
1
(J-20)+(B-20) = \frac{5}{9}(J+B) \implies S-40 = \frac{5}{9}S \implies 9S-360=5S \implies 4S=360 \implies S=90$
So $J+B=90$
2
$J = B+20$
Substitute J: $(B+20)+B = 90 \implies 2B = 70 \implies B=35$
Ajay's age is $J=35+20=55$.

Q14: Ten years ago, the age of a man was 20 years less than 6 times his son's age. Ten years hence, his age will be 30 years less than thrice his son's age. After how many years from now will their combined age be 90 years?

1. 5
2. 10
3. 15
4. 20

Correct Option: B

Correct Answer: 10

Explanation:
Let present ages be M and S
1
$M-10 = 6(S-10)-20 \implies M-6S = -70$ 2
$M+10 = 3(S+10)-30 \implies M-3S = -10$ Solving gives S=20 and M=50
Their current combined age is 70
To reach a combined age of 90, they need to age a combined 20 years
Since they both age, it will take $20/2 = 10$ years.

Q15: A two-digit number is formed by either subtracting 16 from eight times the sum of the digits or by adding 20 to 22 times the difference of the digits. Find the number.

1. 24
2. 48
3. 64
4. 82

Correct Option: C

Correct Answer: 64

Explanation:
Let the number be 10t+u
1
$10t+u = 8(t+u)-16 \implies 2t-7u = -16$ 2
$10t+u = 22(t-u)+20 \implies -12t+23u = 20$ Multiply the first equation by 6: $12t-42u = -96$
Add this to the second equation: $-19u = -76 \implies u=4$. Substitute u=4 into the first equation: $2t - 7(4) = -16 \implies 2t=12 \implies t=6$
The number is 64.

Q16: If $x/4$ years ago, Alok was 14 years old and $x/4$ years from now he will be 4x years old, how old will he be 5x years from now? (in years)

Correct Option:

Correct Answer: 35

Explanation:
Let Alok's present age be A
1
$A - x/4 = 14$ 2
$A + x/4 = 4x$ Adding both equations gives $2A = 14 + 4x \implies A = 7 + 2x$. Substituting A in the first equation: $(7+2x) - x/4 = 14 \implies 7x/4 = 7 \implies x=4$. Alok's present age $A = 7 + 2(4) = 15$. His age 5x (i.e., 20) years from now will be $15 + 20 = 35$.

Q17: Two boys and two girls went to a movie. They found that there were only two tickets available in the counter and they bought them. For purchasing the remaining two tickets (in black), they spent ₹50 more for each ticket than the actual price. At the end they found that each person had spent ₹60 for the ticket as his/her share. Find the actual price (in ₹) of each ticket.

Correct Option:

Correct Answer: 35

Explanation:
There are 4 people, and the average cost per person was ₹60
Total amount spent = $4 \times 60 = ₹240$. Let the actual price of a ticket be P
Total cost = (2 \times P) + 2 \times (P + 50). $240 = 2P + 2P + 100 \implies 140 = 4P \implies P = 35$.

Q18: There are two two-digit numbers such that the tens digit of the first number is $3/2$ times the tens digit of the second number, while the sum of the two numbers is 158. Which of the following can be the difference between them?

1. 58
2. 71
3. 36
4. 40

Correct Option: C

Correct Answer: 36

Explanation:
Let the numbers be $N_1 = 10a+b$ and $N_2 = 10c+d$
$a = \frac{3}{2}c$
The only digit pair (a,c) that allows for a sum of 158 is (9,6). $N_1+N_2 = (90+b) + (60+d) = 158 \implies b+d=8$
The difference is $N_1-N_2 = (90+b) - (60+d) = 30 + (b-d)$
If we choose b=7 and d=1 (which satisfies b+d=8), the difference is $30 + (7-1) = 36$.

Q19: In a three-digit number, the difference between hundreds digit and the tens digit is equal to the difference between the tens digit and the units digit. If the sum of the digits is 9, how many numbers satisfy the given condition?

Correct Option:

Correct Answer: 6

Explanation:
Let the digits be h, t, u
1
h-t = t-u \implies h+u=2t
(The digits are in an arithmetic progression). 2
h+t+u = 9. Substitute h+u from (1) into (2): $(2t) + t = 9 \implies 3t=9 \implies t=3$. Now, $h+u=6$
The possible numbers (where h≠0) are: 135, 234, 333, 432, 531, 630
There are 6 such numbers.

Q20: The difference between a three-digit number and the number formed by reversing its digits is 792. The sum of its digits is 18 and the hundreds digit is 9 times its units digit. Find the number.

Correct Option:

Correct Answer: 981

Explanation:
Let the number be 100h+10t+u. 1
$99(h-u) = 792 \implies h-u = 8$. 2
h=9u. Solving these two gives u=1 and h=9. 3
h+t+u = 18 \implies 9+t+1 = 18 \implies t=8. The number is 981.

Q21: Mr. Ram distributed a total of 225 chocolates among his sons A, B, C and D. The number of chocolates he gave to A and D together is twice the number of chocolates he gave to B and C together. If B received 15 more chocolates than C, find the number of chocolates C received.

Correct Option:

Correct Answer: 30

Explanation:
Total: (A+D) + (B+C) = 225. 1
A+D = 2(B+C)
Substitute this into the total: $2(B+C) + (B+C) = 225 \implies 3(B+C) = 225 \implies B+C = 75$. 2
B = C+15. Substitute B: $(C+15)+C=75 \implies 2C=60 \implies C=30$.

Q22: If the numerator of a fraction is increased by two and the denominator by one, the fraction becomes $13/15$. If the numerator and the denominator are each decreased by four, the fraction becomes 4/5. Find the fraction.

1. $9/24$
2. $13/19$
3. $24/29$
4. None of these

Correct Option: C

Correct Answer: 24/29

Explanation:
Let the fraction be N/D. 1
(N+2)/(D+1) = 13/15 \implies 15N - 13D = -17. 2
(N-4)/(D-4) = 4/5 \implies 5N - 4D = 4. Multiplying the second equation by 3 gives 15N - 12D = 12. Subtracting this from the first gives -D = -29 \implies D=29. Then 5N - 4(29) = 4 \implies 5N = 120 \implies N=24
The fraction is 24/29.

Q23: Ajay and Sita are two of Mr.Sharma's children. Ajay has half as many brothers as sisters. Sita has as many brothers as sisters. Find the number of children Mr.Sharma has.

Correct Option:

Correct Answer: 7

Explanation:
Let b be the number of boys and g be the number of girls. 1
From Ajay's (a boy) perspective: (b-1) = \frac{1}{2}g \implies 2b-2 = g. 2
From Sita's (a girl) perspective: b = g-1 \implies g=b+1. Equating the expressions for g: $2b-2 = b+1 \implies b=3$. Then $g = 3+1 = 4$
Total children = 3+4=7.

Q24: Rohan went to the market to buy 10 kg of each of oranges, mangoes, bananas and grapes. The cost of 5 kg oranges and 2 kg mangoes together was ₹310. The cost of 3 kg mangoes and 3.5 kg bananas together was ₹230. The cost of 1.5 kg bananas and 5 kg grapes together was ₹160. Find the total amount spent by Rohan (in ₹).

Correct Option:

Correct Answer: 1400

Explanation:
Let the costs per kg be O, M, B, G
We have: 1
5O + 2M = 310 2
3M + 3.5B = 230 3
1.5B + 5G = 160 Adding all three equations: 5O + (2M+3M) + (3.5B+1.5B) + 5G = 310+230+160. $5O + 5M + 5B + 5G = 700 \implies O+M+B+G = 140$. Total cost for 10kg of each is $10(O+M+B+G) = 10(140) = 1400$.

Q25: If he bought less than 15 bananas, how many oranges did he buy?

Correct Option:

Correct Answer: 18

Explanation:
Given: o > b > a, a, b, o >= 13, a+b+o = 45. Condition: b < 15
Since b >= 13, b must be 13 or 14
If b=13, then a must be <13, which violates a>=13. Therefore, b must be 14
Then a must be 13 (as a < b and a >= 13). $o = 45 - a - b = 45 - 13 - 14 = 18$.

Q26: The cost of an apple, a banana and an orange is ₹5, ₹4 and ₹3 respectively. What is the minimum possible expenditure (in ₹) that Arjun could have incurred?

Correct Option:

Correct Answer: 175

Explanation:
From the conditions o > b > a, a,b,o >= 13, a+b+o = 45, we want to minimize 5a + 4b + 3o. To minimize the cost, we should buy the fewest expensive items (apples) and the most cheap items (oranges). This means we should choose the smallest possible values for a and b. Min a=13, min b=14
This gives o=18. Expenditure = $5(13) + 4(14) + 3(18) = 65 + 56 + 54 = 175$.

Q27: If a, b, c and d satisfy the equations $a+7b+3c+5d=0$, $8a+4b+6c+2d=-16$, $a+6b+4c+8d=16$ and $5a+3b+7c+d=-16$ then (a+d)(b+c) equals

1. 0
2. 16
3. -16
4. -64

Correct Option: C

Correct Answer: -16

Explanation:
Let the four equations be (1), (2), (3), (4). Add (1) and (4): $6a+10b+10c+6d = -16 \implies 3(a+d)+5(b+c) = -8$
(Eq
A) Add (2) and (3): $9a+10b+10c+10d = 0 \implies 9a+10(b+c)+10d=0$
(Eq
B) Let $X=a+d$ and $Y=b+c$
Then $3X+5Y=-8$
A possible integer solution is X=4, Y=-4
Test this in Eq
B: $9a+10(-4)+10d=0 \implies 9a+10d=40$
Using $a+d=4 \implies d=4-a$, we get $9a+10(4-a)=40 \implies -a=0 \implies a=0$
This is consistent
So $a+d=4$ and $b+c=-4$
The product is $(4)(-4) = -16$.

Q28: Considering the equations $2x-3y=8$ and $px-qy=66$ answer the following questions: (i) Find 4(p+q) if the equations above have infinite solutions. (ii) Find p if q=9 and the equations above have no solution.

Correct Option:

Correct Answer: (i) 165 (ii) 6

Explanation:
For a system $a_1x+b_1y=c_1, a_2x+b_2y=c_2$: (i) Infinite Solutions: $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
$\frac{2}{p} = \frac{-3}{-q} = \frac{8}{66} \implies \frac{2}{p} = \frac{3}{q} = \frac{4}{33}$
This gives $p = 33/2$ and $q = 99/4$
$4(p+q) = 4(\frac{66}{4}+\frac{99}{4}) = 165$
(ii) No Solution: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
$\frac{2}{p} = \frac{-3}{-9} \implies \frac{2}{p} = \frac{1}{3} \implies p = 6$
(Check: $\frac{1}{3} \neq \frac{8}{66}$, condition holds).

Q29: nan

Correct Option:

Correct Answer:

Explanation:

Q30: In a four-digit number with distinct digits, the sum of the middle digits equals the sum of the extreme digits. The sum of its second and fourth digits equals five times the sum of its other two digits. If the sum of its digits is 18, what is the sum of all the possible values of the hundreds digit?

1. 21
2. 24
3. 27
4. 30

Correct Option: B

Correct Answer: 24

Explanation:
Let the number be abcd. 1
$b+c = a+d$ 2
$a+b+c+d=18 \implies 2(b+c)=18 \implies b+c=9$
This also means $a+d=9$. 3
$b+d = 5(a+c) Substitute c=9-b and d=9-a into the third equation: $b+(9-a) = 5(a+(9-b)) \implies 6b-6a=36 \implies b-a=6$. Possible pairs for (a,b) are (1,7), (2,8), (3,9)
These give the numbers 1728, 2817, and 3906. The possible values for the hundreds digit (b) are 7, 8, and 9
The sum is $7+8+9=24$.

Q31: A two-digit number is obtained by either subtracting 12 from four times the sum of its digits or by adding 6 to twice the difference of its digits. Find the number.

1. 16
2. 28
3. 39
4. Cannot be determined

Correct Option: A

Correct Answer: 16

Explanation:
Let the number be 10t+u. 1
$10t+u = 4(t+u)-12 \implies 6t-3u=-12 \implies 2t-u=-4$. 2
$10t+u = 2(u-t)+6 \implies 12t-u=6$
(Assuming u>t). Subtracting the first equation from the second gives $10t=10 \implies t=1$. From 2t-u=-4, we get $2(1)-u=-4 \implies u=6$
The number is 16.

Q32: Ramu has some chocolate boxes with him to sell. He sells them either as full boxes or half boxes. The first customer buys half a box more than half the number of boxes with Ramu. The second customer buys half a box more than half the remaining number of boxes with him. Ramu continues to sell in this manner to eight other customers. He is left with no boxes to sell after that. How many chocolate boxes did Ramu have in the beginning?

1. 511
2. 513
3. 1023
4. 1025

Correct Option: C

Correct Answer: 1023

Explanation:
This problem involves 10 customers in total
Let C_n be the number of boxes before customer n
The number left after customer n is C_n - (0.5 C_n + 0.5) = 0.5 C_n - 0.5. So, C_{n+1} = 0.5 C_n - 0.5, which means $C_n = 2 C_{n+1} + 1$. Working backwards from C_{11}=0 (after 10 customers): $C_{10} = 2(0)+1=1$. $C_9 = 2(1)+1=3$. $C_8 = 2(3)+1=7$. The pattern is $C_{11-k} = 2^k - 1$
For the beginning amount (C_1), k=10. Initial boxes = $2^{10} - 1 = 1024 - 1 = 1023$.

Q33: Alok went to a casino to play a card game. He played 10 rounds of that game. In each round, he doubled his amount and then gave x to his friend. After 10 rounds, he had ₹1023. Find the sum of the digits of the least possible value of x. (All the amounts involved (in rupees) are integers)

Correct Option:

Correct Answer: 6

Explanation:
Let the initial amount be $A_0$
The amount after n rounds is $A_n = 2^n A_0 - (2^n - 1)x$. After 10 rounds, $A_{10} = 2^{10}A_0 - (2^{10}-1)x = 1024A_0 - 1023x$. We are given $1024A_0 - 1023x = 1023$. $1024A_0 = 1023(x+1)$. Since 1024 and 1023 are coprime, $x+1$ must be a multiple of 1024
The least positive integer value for x occurs when $x+1=1024 \implies x=1023$. The sum of the digits of x is $1+0+2+3=6$.

Q34: How many possibilities exist for the actual number of toys sold?

Correct Option:

Correct Answer: 1

Explanation:
Let the actual number of toys be N=10a+b
The mistaken number is N'=10b+a
The computer stock showed 81 more items left, which means the recorded number of sales was 81 less than actual. $N - N' = 81$ $(10a+b) - (10b+a) = 81$ $9a - 9b = 81 \implies a - b = 9$. Since a and b are single digits and a cannot be 0, the only possibility is a=9, b=0
This gives only 1 possible value for the number of toys sold (N=90).

Q35: If the faulty calculations show a total sale of ₹486, what was the actual selling price (in ₹) of each toy?

Correct Option:

Correct Answer: 45

Explanation:
From the previous analysis, the actual number of toys sold was N=90, so the faulty number sold was N'=09=9. Faulty Sale = Faulty Number × Faulty Price = 486. $9 \times P' = 486 \implies P' = 54$. The faulty price P' = 10d+c = 54, so d=5 and c=4. The actual selling price is P = 10c+d = 10(4)+5 = 45.

Q36: Raja went to a casino to play a card game. He played 3 rounds of the game. In each round he doubled the amount he had with him and gave X to his friend at the end of the round. The amount he had with him at the end of the third round after giving X to his friend was ₹140 more than the sum of the amounts with him at the end of the previous rounds after giving X to his friend. The amount with him at the end of the second round after giving X to his friend was ₹160 more than the amount he had with him at the end of the first round after giving X to his friend. Find the value of X.

1. 10
2. 20
3. 30
4. 40

Correct Option: B

Correct Answer: 20

Explanation:
Let A1, A2, A3 be the amounts after rounds 1, 2, and 3. 1
$A2 = 2A1 - X$ 2
$A3 = 2A2 - X$ Given conditions: 3
$A2 = A1 + 160$ 4
$A3 = (A1+A2)+140$ From (1) and (3): $A1+160 = 2A1-X \implies A1 = X+160$. Now find A2 and A3 in terms of X: $A2 = (X+160)+160 = X+320$. $A3 = 2(X+320)-X = X+640$. Substitute into (4): $X+640 = (X+160)+(X+320)+140 \implies X+640 = 2X+620 \implies X=20$.

Q37: If $x+2y+3z=14$, then find the value of z. I. $x+3y+z=14$ II. $3x+y+2z=11$

Correct Option: C

Correct Answer: (C)

Explanation:
With the initial equation, we have 1 equation and 3 unknowns
We need two more independent equations. Statement I alone gives a second equation
Subtracting it from the given equation yields y-2z=0, but we cannot find z
Insufficient. Statement II alone gives a second equation
We still have 2 equations and 3 unknowns
Insufficient. Using both statements I and II together with the initial equation gives a system of 3 linear equations with 3 variables, which can be solved for a unique value of z
Sufficient.

Q38: Guru had some one-rupee coins, 50-rupee notes and 100-rupee notes. He exchanged all his coins for 50-rupee and 100-rupee notes (not by value, only by number). After the exchange, Guru has ₹500. How many 50-rupee notes does he have after the exchange? I. He has not more than 6 notes after the exchange. II. He has not less than 6 notes after the exchange.

Correct Option: A

Correct Answer: (A)

Explanation:
Let f be the number of ₹50 notes and h be the number of ₹100 notes after exchange
The total value is $50f + 100h = 500 \implies f+2h=10$
Possible integer solutions (f, h) are (8,1), (6,2), (4,3), (2,4). Statement I: Total notes (f+h) <= 6
This is only satisfied by the solution (2,4), where f+h=6
So f=2
Sufficient. Statement II: Total notes (f+h) >= 6
This is satisfied by all four solutions
So f could be 2, 4, 6, or 8
Insufficient.

Q39: What is my age? I. Five years ago, my sister's age was half of my age. II. Five years from now, my sister's age will be three fourths of my age.

Correct Option: C

Correct Answer: (C)

Explanation:
Let my age be M and my sister's be S. Statement I: S-5 = (M-5)/2
One equation, two variables
Insufficient. Statement II: S+5 = 3(M+5)/4
One equation, two variables
Insufficient. Together, we have a system of two independent linear equations with two variables (2S-M=5 and 4S-3M=-5), which can be solved for unique values of M and S
Sufficient.

Q40: How many questions did I attempt in a maths test having 25 questions? I. I scored 16 marks. II. For every correct answer I got 1 mark while for every incorrect answer I lost $\frac{1}{4}$ mark.

Correct Option: D

Correct Answer: (D)

Explanation:
Let c, w, u be correct, wrong, unanswered
We need c+w
c+w+u=25. Statement I gives the score but not the marking scheme
Insufficient. Statement II gives the marking scheme but not the score
Insufficient. Together: c - (w/4) = 16 \implies 4c-w=64
We also have c+w \leq 25. If c=16, w=0, so c+w=16
If c=17, w=4, so c+w=21
Since there are multiple possible values for the number of attempted questions, the information is insufficient.

Q41: If $3x+7y=19$, then find the value of y. I. $6x+14y=38$ II. $9x-20y=16$

Correct Option: A

Correct Answer: (A)

Explanation:
Statement I: $6x+14y=38$ simplifies to $3x+7y=19$
This is the same as the given equation and provides no new information
Insufficient. Statement II: We now have a system of two different linear equations: 3x+7y=19 and 9x-20y=16
This system can be solved for a unique value of y
Sufficient. Since the question can be answered by II alone but not by I alone, the correct option is (A).

Daily Current Affairs - 22 June 2025

Daily Current Affairs - 22 June 2025

Styled like your website cards: clean image, bold headline, crisp summary.

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