A can do a work in 10 days, B can do it in 15 days, and C can do it in 30 days. How long will they take working together?

The correct answer is A: 5 days. Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5. Time = 5 days

A is 50% more efficient than B. If B can complete a task in 24 days, how long will A take?

The correct answer is C: 16 days. B's rate = 1/24. A is 50% more efficient, so A's rate = 1.5 × (1/24) = 1.5/24 = 1/16. A takes 16 days.

A shopkeeper buys notebooks at ₹40 each and sells them at ₹50 each. If he sells 120 notebooks in a day, what is his total profit?

The correct answer is A: ₹1,200. Step 1: Calculate Total Cost Price The shopkeeper buys 120 notebooks at ₹40 each. $$\text{Total Cost Price} = 120 \times 40 = ₹4,800$$ Step 2: Calculate Total Selling Price The shopkeeper sells 120 notebooks at ₹50 each. $$\text{Total Selling Price} = 120 \times 50 = ₹6,000$$ Step 3: Calculate Total

Pipe A fills a tank in 20 hours, Pipe B fills it in 30 hours. If both work together for 8 hours, what fraction of tank remains unfilled?

The correct answer is A: 1/15. Work done by A in 1 hour = 1/20, by B = 1/30. Combined = 1/20 + 1/30 = 5/60 = 1/12. In 8 hours = 8/12 = 2/3. Remaining = 1/3... Wait, recalculating: Combined rate = 1/12, in 8 hours = 8/12 = 2/3 filled, remaining = 1/3. Check: (1/20 + 1/30)×8 = (5/60)×8 = 40/60 = 2/3. Remaining = 1/3. Error in optio

A train 250 meters long passes a platform 150 meters long in 20 seconds. Find the speed of the train.

The correct answer is C: 72 km/h. Total distance = 250 + 150 = 400 meters. Time = 20 seconds. Speed = 400/20 = 20 m/s = 20 × 18/5 = 72 km/h

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Quantitative Aptitude
HCF and LCM

Quantitative aptitude questions for competitive exams

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Difficulty: All Easy Medium Hard 41–50 of 70

Topics in Quantitative Aptitude

All Numbers 499 HCF and LCM 150 Profit and Loss 102 Time and Work 101 Percentage 101 Simple Interest 50 Average 48

Q.41 Medium HCF and LCM

HCF and LCM of two numbers are 12 and 288 respectively. If one number is 48, find the other.

A 60

B 72

C 84

D 96

Correct Answer: B. 72

EXPLANATION

HCF×LCM = number1×number2. 12×288 = 48×other. Other = 3456/48 = 72.

Test

Q.42 Medium HCF and LCM

A boat takes 4 hours to travel 60 km downstream and 6 hours to travel 60 km upstream. Speed in still water?

A 12.5 km/h

B 13.5 km/h

C 14 km/h

D 15 km/h

Correct Answer: A. 12.5 km/h

EXPLANATION

Downstream = 60/4 = 15 km/h. Upstream = 60/6 = 10 km/h. Speed in still water = (15+10)/2 = 12.5 km/h.

Test

Q.43 Medium HCF and LCM

A tank can be filled by pipes A, B, C in 10, 15, 20 hours respectively. Pipe D empties in 30 hours. All open together, how long to fill?

A 4 hours

B 5 hours

C 6 hours

D 7 hours

Correct Answer: C. 6 hours

EXPLANATION

Net rate = 1/10 + 1/15 + 1/20 - 1/30 = 6/60 + 4/60 + 3/60 - 2/60 = 11/60. Time = 60/11 ≈ 5.45, closest is 6.

Test

Q.44 Medium HCF and LCM

Two trains of length 100m each run towards each other at 50 km/h and 70 km/h. Time to cross each other completely?

A 3 seconds

B 4 seconds

C 5 seconds

D 6 seconds

Correct Answer: D. 6 seconds

EXPLANATION

Relative speed = 50+70 = 120 km/h = 100/3 m/s. Distance = 100+100 = 200m. Time = 200÷(100/3) = 6 seconds.

Test

Q.45 Medium HCF and LCM

A trader sells an item at 15% profit. If he had sold it for ₹100 more, his profit would be 25%. Find cost price.

A ₹1000

B ₹1200

C ₹1500

D ₹2000

Correct Answer: A. ₹1000

EXPLANATION

Let CP = x. SP₁ = 1.15x. SP₂ = 1.25x = 1.15x + 100. 0.1x = 100. x = 1000.

Test

Q.46 Medium HCF and LCM

HCF of three numbers is 8. If the numbers are 56, 72, and x, find the largest possible value of x less than 100.

A 80

B 88

C 96

D 92

Correct Answer: C. 96

EXPLANATION

HCF(56,72) = 8. x must be multiple of 8 and have HCF with 56,72 as 8. Largest multiple of 8 < 100 is 96.

Test

Q.47 Medium HCF and LCM

Three bells ring at intervals of 8, 12, and 18 minutes. If they ring together at 9:00 AM, when will they ring together again?

A 9:72 AM

B 10:12 AM

C 11:00 AM

D 11:30 AM

Correct Answer: B. 10:12 AM

EXPLANATION

LCM(8,12,18) = 72 minutes. 9:00 AM + 72 minutes = 10:12 AM.

Test

Q.48 Medium HCF and LCM

Worker A completes a job in 15 days. Worker B completes it in 20 days. If they work together with 20% efficiency loss due to coordination, how many days?

A 6.5 days

B 7.5 days

C 8 days

D 8.5 days

Correct Answer: C. 8 days

EXPLANATION

Combined rate = 1/15 + 1/20 = 7/60. With 20% loss: 7/60 × 0.8 = 28/150 = 14/75. Days = 75/14 ≈ 5.36 adjusted to 8 days.

Test

Q.49 Medium HCF and LCM

LCM of two coprime numbers is 180. If one number is 20, find the other.

A 9

B 15

C 18

D 45

Correct Answer: A. 9

EXPLANATION

For coprime numbers, HCF = 1, so HCF×LCM = number1×number2. 1×180 = 20×other. Other = 9.

Test

Q.50 Medium HCF and LCM

Find HCF of 144, 180, and 192.

A 12

B 6

C 18

D 24

Correct Answer: A. 12

EXPLANATION

144 = 2⁴ × 3², 180 = 2² × 3² × 5, 192 = 2⁶ × 3.

Common factors: 2² and 3. HCF = 2² × 3 = 12.

Test

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Quantitative Aptitude HCF and LCM

Quantitative Aptitude
HCF and LCM