CAPF AC 2025 Q66: General Mental Ability – Quantitative Aptitude

CAPF AC 2025, Paper I (General Ability and Intelligence) · General Mental Ability

Two trains A and B are entering a railway platform from opposite direction. The length of the platform is 300 m. The speed of B is two times the speed of A. The time taken by B to cross the platform is one-third of the time taken by A to cross the platform. If the sum of the lengths of A and B is 500 m, what is the difference in their lengths?

(a) 220 m
(b) 250 m
(c) 200 m
(d) 300 m

Answer: (a) 220 m

Explanation

Two trains and a platform

Given: platform length 300 m. Speed of B = 2 × speed of A. Time for B to cross the platform = one-third of the time for A. Length of A + length of B = 500 m.

How to think: time to cross a platform = (train length + 300) ÷ speed.

Let A's speed be v, so B's is 2v.

Step	Working	Result
Time for A	(L_A + 300) ÷ v	Train plus platform, over speed
Time for B	(L_B + 300) ÷ 2v	Same, with double the speed
B's time is one-third of A's	(L_B + 300) ÷ 2 = (L_A + 300) ÷ 3	3 L_B + 900 = 2 L_A + 600
Simplify	2 L_A − 3 L_B = 300	One equation in the two lengths
Use L_A + L_B = 500	2(500 − L_B) − 3 L_B = 300	L_B = 140, L_A = 360
Difference	360 − 140	220 m

Check: A takes (360 + 300) ÷ v = 660/v; B takes (140 + 300) ÷ 2v = 220/v, which is one-third of 660/v. ✓

Bank key corrected: the stored key was (c) 200 m; the right answer is (a) 220 m.

Answer: (a) 220 m.

Why each option is right or wrong

(a) CORRECT. The lengths are 360 m and 140 m, so the difference is 220 m.
(b) Incorrect. A difference of 250 m would give lengths 375 and 125, which fail the time condition.
(c) Incorrect. A difference of 200 m would give lengths 350 and 150, which fail the time condition.
(d) Incorrect. A difference of 300 m would give lengths 400 and 100, which fail the time condition.

Key point

Time to cross a platform = (train length + platform length) ÷ speed. Here (L_B + 300)/2v = (L_A + 300)/(3v), and L_A + L_B = 500, so L_A = 360, L_B = 140, difference 220 m.

Remember

(length + 300)/speed: B's time is a third of A's with double the speed, giving 360 m and 140 m.

Common mistakes

Forgetting to add the platform length (300 m) to each train's length.
Using the time ratio the wrong way round, so B takes three times as long.
Treating the two trains as crossing each other instead of the platform.

Exam tip

Educated guess: the lengths add to 500, so the difference and the sum must have the same parity. All four options are even, so try each: only 220 gives lengths (360, 140) that satisfy the time ratio.

Sources

R. S. Aggarwal, Quantitative Aptitude for Competitive Examinations, chapter on Problems on Trains
NCERT Class X Mathematics, Chapter 3 (Pair of Linear Equations in Two Variables)

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