CAPF AC 2022 Q32: General Mental Ability – Quantitative Aptitude

CAPF AC 2022, Paper I (General Ability and Intelligence) · General Mental Ability

1. (a) 40
2. (b) 30
3. (c) 100/3
4. (d) 35

Answer: (c) 100/3

Explanation

Average speed over two parts of a journey

Given: a car covers 3/4 of the distance at 60 km/hr and the remaining 1/4 at v km/hr; the average speed is 50 km/hr; find v.

How to think: average speed is total distance ÷ total time.

Pick an easy distance and add the times.

Let the distance be 200 km.

Time for the last part: 4 − 2.5 = 1.5 hours.

So v = 50 ÷ 1.5 = 100/3 km/hr, which is about 33.3 km/hr.

Answer: (c) 100/3.

Why each option is right or wrong

• (a) Incorrect. At 40 km/hr the last part takes 1.25 hours and the average is over 53 km/hr.
• (b) Incorrect. At 30 km/hr the last part takes 1.67 hours and the average is 48 km/hr.
• (c) CORRECT. The last 50 km must take 1.5 hours, so v = 100/3 km/hr.
• (d) Incorrect. At 35 km/hr the average works out to about 50.9 km/hr, not 50.

Key point

Average speed = total distance ÷ total time, never the plain average of the speeds. Assume a convenient total distance and add the times.

Remember

Average speed: add the times, not the speeds.

Common mistakes

• Using a weighted average of the speeds (3/4 × 60 + 1/4 × v = 50), which gives 20.
• Averaging the two speeds directly and solving (60 + v)/2 = 50.
• Forgetting that the slower part takes more time than its share of distance.

Exam tip

Educated guess: the answer is an awkward fraction only when times are being divided. An option like 100/3 among whole numbers is a hint that the proper time-based method lands there.

Sources

• NCERT Class VII Science — Motion and Time (speed)
• R. S. Aggarwal, Quantitative Aptitude — Time and Distance

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