Quantitative Aptitude — Numbers Questions & Answers

Q.1 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.2 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.3 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.4 Medium Numbers

Pipe A fills a tank in 15 hours, Pipe B in 20 hours, and Pipe C empties it in 30 hours. If all three work together, how long to fill the tank?

A 8 hours

B 10 hours

C 12 hours

D 15 hours

Correct Answer: C. 12 hours

EXPLANATION

Combined rate = 1/15 + 1/20 - 1/30 = (4+3-2)/60 = 5/60 = 1/12. Time = 12 hours

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Q.5 Easy Numbers

A sum becomes 4 times itself in 15 years at simple interest. What is the rate of interest per annum?

A 15%

B 20%

C 25%

D 30%

Correct Answer: B. 20%

EXPLANATION

If sum becomes 4 times, SI = 3P. SI = P×R×T/100 → 3P = P×R×15/100 → R = 20% p.a.

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Q.6 Easy Numbers

A shopkeeper marks goods at 60% above cost price. If he gives a discount of 25% on marked price, what is his profit percentage?

A 20%

B 25%

C 30%

D 35%

Correct Answer: A. 20%

EXPLANATION

Let CP = 100. MP = 160. After 25% discount, SP = 160 × 0.75 = 120. Profit% = (120-100)/100 × 100 = 20%

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Q.7 Hard Numbers

A vendor buys oranges at Rs. 40 per dozen and sells at 5 per rupee. What is his loss percentage?

A 30%

B 33.33%

C 40%

D 45%

Correct Answer: B. 33.33%

EXPLANATION

CP per unit = 40/12 = 10/3. SP per unit = 1/5. Loss = (10/3 - 1/5)/(10/3) × 100 = 33.33%

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Q.8 Hard Numbers

A pipe fills a tank in 12 hours, another pipe empties it in 15 hours. With both open, net fill time?

A 50 hours

B 55 hours

C 60 hours

D 65 hours

Correct Answer: C. 60 hours

EXPLANATION

Net rate = 1/12 - 1/15 = (5-4)/60 = 1/60. Time = 60 hours

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Q.9 Hard Numbers

A man invests Rs. 4000 for 3 years. Part at 5% and remaining at 7% p.a. simple interest. Total interest = Rs. 820. Amount at 5%?

A Rs. 1500

B Rs. 2000

C Rs. 2500

D Rs. 3000

Correct Answer: C. Rs. 2500

EXPLANATION

Let amount at 5% = x. Then (x × 5 × 3)/100 + ((4000-x) × 7 × 3)/100 = 820. Solving: x = 2500

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Q.10 Hard Numbers

Two trains of lengths 150m and 100m run on parallel tracks at 60 km/h and 40 km/h respectively in opposite directions. Time to cross each other?

A 9 seconds

B 10 seconds

C 15 seconds

D 18 seconds

Correct Answer: D. 18 seconds

EXPLANATION

Relative speed = 60 + 40 = 100 km/h = 100 × 5/18 = 250/9 m/s. Total length = 250m. Time = 250/(250/9) = 9 seconds. But let me recalculate: 250 ÷ (250/9) = 9. Answer should be A, not D.

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