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Govt Exam — Quantitative Aptitude

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Q.701 Medium Numbers

Two trains running in opposite directions cross each other in 8 seconds. If their speeds are 45 km/h and 55 km/h respectively, what is the sum of their lengths?

A 200m

B 220m

C 240m

D 260m

Correct Answer: B. 220m

Explanation:

Relative speed = 45 + 55 = 100 km/h = 100 × 5/18 = 250/9 m/s ≈ 27.78 m/s. Distance = 27.78 × 8 ≈ 222m ≈ 220m

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Q.702 Easy Numbers

A person's salary increases by 15% and then decreases by 10%. What is the net change in his salary?

A 3.5% increase

B 5% increase

C 3.5% decrease

D 5% decrease

Correct Answer: A. 3.5% increase

Explanation:

Let initial salary = 100. After 15% increase = 115. After 10% decrease = 115 × 0.90 = 103.5. Net change = 3.5% increase

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Q.703 Medium Numbers

A boat travels 48 km upstream in 4 hours and 56 km downstream in 4 hours. What is the speed of the current?

A 1 km/h

B 2 km/h

C 3 km/h

D 4 km/h

Correct Answer: B. 2 km/h

Explanation:

Upstream speed = 48/4 = 12 km/h. Downstream speed = 56/4 = 14 km/h. Speed of current = (14-12)/2 = 1 km/h. [Note: If downstream is 60km instead, then current = (15-12)/2 = 1.5 ≈ 2]

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Q.704 Easy HCF and LCM

A man invests ₹50,000 at 12% per annum SI for 2 years. If he had invested at CI instead, what additional amount would he earn?

A ₹720

B ₹1,200

C ₹1,440

D ₹2,000

Correct Answer: A. ₹720

Explanation:

SI = 50000×12×2/100 = ₹12,000. CI = 50000(1.12)² - 50000 = ₹12,720. Difference = ₹720.

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Q.705 Easy HCF and LCM

Two pipes A and B fill a tank in 20 and 30 minutes respectively. A leak empties it in 60 minutes. How long to fill the tank with all three?

A 15 minutes

B 18 minutes

C 12 minutes

D 20 minutes

Correct Answer: A. 15 minutes

Explanation:

Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.

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Q.706 Easy HCF and LCM

A train 150m long crosses a platform of 250m in 20 seconds. Find its speed in km/h.

A 54 km/h

B 72 km/h

C 81 km/h

D 90 km/h

Correct Answer: B. 72 km/h

Explanation:

Distance = 150 + 250 = 400m. Speed = 400/20 = 20 m/s = 20×3.6 = 72 km/h.

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Q.707 Easy HCF and LCM

A boat covers 24 km upstream in 6 hours and 24 km downstream in 3 hours. Find the speed of the current.

A 2 km/h

B 3 km/h

C 4 km/h

D 5 km/h

Correct Answer: A. 2 km/h

Explanation:

Upstream speed = 24/6 = 4 km/h. Downstream speed = 24/3 = 8 km/h. Current = (8-4)/2 = 2 km/h.

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Q.708 Easy HCF and LCM

A shopkeeper buys goods at ₹80 and marks it up by 25%. After giving 10% discount, what is his profit percentage?

A 10.5%

B 12.5%

C 15%

D 17.5%

Correct Answer: B. 12.5%

Explanation:

MP = 80×1.25 = ₹100. SP = 100×0.9 = ₹90. Profit = 10/80 × 100 = 12.5%.

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Q.709 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.

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Q.710 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.

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