CAPF AC 2023 Q43: General Mental Ability – Quantitative Aptitude

CAPF AC 2023, Paper I (General Ability and Intelligence) · General Mental Ability

1. (a) 75
2. (b) 90
3. (c) 105
4. (d) 120

Answer: (b) 90

Explanation

Three taps draining a tank

Given: the draining capacities of A, B, C are in the ratio 1 : 2 : 3, and all three together empty the full tank in 1 hour (60 minutes).

How to think: treat the ratio as units of work per hour.

A does 1 unit, B does 2 units, C does 3 units, so all three do 6 units per hour.

That 6 units empties the tank in 1 hour, so the tank holds 6 units.

Check: B alone drains 2 units an hour, so removing B slows the draining by one-third, and 60 minutes becomes 60 × 6/4 = 90 minutes.

Answer: (b) 90.

Why each option is right or wrong

• (a) Incorrect. 75 minutes would need A and C to do 4.8 units per hour, not 4.
• (b) CORRECT. A and C do 4 of the 6 units an hour, so the tank takes 90 minutes.
• (c) Incorrect. 105 minutes does not match 4 units per hour for a 6-unit tank.
• (d) Incorrect. 120 minutes would be the time at 3 units an hour, only C working.

Key point

Rate method: capacity ratio 1 : 2 : 3, total rate 6 units/hr in 60 minutes. A + C = 4 units/hr. Time = 6 ÷ 4 = 1.5 h = 90 minutes. Time is inversely proportional to rate.

Remember

Rates add: 1 + 3 = 4 of 6, so time = 60 × 6/4.

Common mistakes

• Taking the ratio as times instead of rates; a bigger ratio means a faster tap.
• Subtracting only B's share of the time instead of its share of the rate.
• Stopping at 1.5 and not converting hours to minutes.

Exam tip

Educated guess: removing the middle tap leaves 4 of the 6 parts, so the time grows by 6/4 = 1.5 times. Sixty minutes times 1.5 is the only option that fits, 90.

Sources

• NCERT Class VIII Mathematics — Direct and Inverse Proportions, Chapter 13 (inverse proportion: more rate, less time)
• NCERT Class VI Mathematics — Ratio and Proportion, Chapter 12

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