CAPF AC 2025 Q61: General Mental Ability – Quantitative Aptitude
- (a) 38 km/h
- (b) 30 km/h
- (c) 36 km/h
- (d) 35 km/h
Answer: (c) 36 km/h
Explanation
Two bikers on a highway
Given: P and Q are 300 km apart. Bikers A and B start together from P towards Q; B is 12 km/h slower than A.
A reaches Q, turns back at once and meets B 60 km from Q.
How to think: when they meet, they have travelled for the same time.
A has gone 300 km to Q plus 60 km back = 360 km; B has gone 300 − 60 = 240 km.
In equal time, distances are in the ratio of speeds.
| Step | Working | Result |
|---|---|---|
| Ratio of speeds | A : B = 360 : 240 | 3 : 2 |
| Let B's speed be v | A = v + 12 and A = 1.5 v | 1.5 v = v + 12 |
| Solve | 0.5 v = 12 | v = 24, A = 36 |
Check: A takes 360 ÷ 36 = 10 h; B takes 240 ÷ 24 = 10 h. ✓
Answer: (c) 36 km/h.
Why each option is right or wrong
- (a) Incorrect. At 38 km/h, B's speed would be 26 and the times would not match.
- (b) Incorrect. At 30 km/h, B's speed would be 18 and the times would not match.
- (c) CORRECT. A goes 360 km in the time B goes 240 km, so A = 36 km/h.
- (d) Incorrect. At 35 km/h, B's speed would be 23 and the times would not match.
Key point
Equal time means distance ∝ speed. A: 300 + 60 = 360 km; B: 300 − 60 = 240 km; ratio 3 : 2; A − B = 12 gives B = 24, A = 36 km/h.
Remember
A covers 360 km while B covers 240: speeds 3 : 2, difference 12, so A = 36.
Common mistakes
- Counting A's distance as only 300 km and ignoring the return trip.
- Taking B's distance as 60 km, the gap from Q, instead of 240 km.
- Forgetting to add the 12 km/h difference after finding B's speed.
Exam tip
Educated guess: the speed ratio is 3 : 2, so A's speed must be a multiple of 3 and 12 km/h is one part. 12 × 3 = 36.
Sources
- NCERT Class X Mathematics, Chapter 3 (Pair of Linear Equations in Two Variables: speed, distance, time)
- NCERT Class VI Mathematics, Chapter 12 (Ratio and Proportion)