CAPF AC 2023 Q42: General Mental Ability – Quantitative Aptitude
- (a) 30
- (b) 40
- (c) 45
- (d) 50
Answer: (c) 45
Explanation
Speed of car A
Given: car B travels at 60 km/h. Car A takes 1 hour more than B for the same distance. If A doubled its speed, it would take 1 hour less than B.
How to think: let B take t hours, so the distance is 60t.
Car A takes t + 1 hours at its original speed, and t − 1 hours at double speed.
Doubling the speed halves the time, so the original time is twice the new time.
| Step | Working | Result |
|---|---|---|
| Time at double speed is half the original | t + 1 = 2 × (t − 1) | t + 1 = 2t − 2 |
| Solve for t | t = 3 | B takes 3 h |
| Distance | 60 × 3 | 180 km |
| A's original time | 3 + 1 | 4 h |
| A's original speed | 180 ÷ 4 | 45 km/h |
Check: doubled speed is 90 km/h, time is 180 ÷ 90 = 2 h, which is 1 hour less than B's 3 h.
Answer: (c) 45.
Why each option is right or wrong
- (a) Incorrect. At 30 km/h the time is 6 h; doubled it is 3 h, not 1 hour less than B.
- (b) Incorrect. At 40 km/h the time is 4.5 h; the distance and time clues do not fit.
- (c) CORRECT. 180 km at 45 km/h takes 4 h, and at 90 km/h takes 2 h.
- (d) Incorrect. At 50 km/h the time is 3.6 h, which is not 1 hour more than B.
Key point
Distance = speed × time. Same distance, double speed means half the time. Set up: t + 1 = 2(t − 1), t = 3, distance = 180 km, speed of A = 180 ÷ 4 = 45 km/h.
Remember
Double speed, half time: t + 1 = 2(t − 1).
Common mistakes
- Writing the time of A at double speed as t + 1 instead of t − 1.
- Forgetting that doubling the speed halves the time.
- Stopping at t = 3 and giving B's time or the distance as the answer.
Exam tip
Educated guess: try the options. A's time must be 1 hour more than B's, so the distance is 60 × (A's time − 1). With 45: time 4 h, distance 180 km, and 180 ÷ 60 = 3 h matches. Only (c) satisfies it.
Sources
- NCERT Class X Mathematics — Pair of Linear Equations in Two Variables, Chapter 3 (word problems on speed, distance and time)
- NCERT Class VIII Mathematics — Linear Equations in One Variable, Chapter 2 (word problems)