SSC CGL 2024 Tier-I · 19 September 2024, Shift 1 · Quantitative Aptitude · Question 21 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Two trains of lengths 150 m and 250 m run on parallel lines. When they run in the same direction, they take 20 seconds to cross each other and, when they run in the opposite direction, they take 5 seconds to cross each other. What is the speed of the two trains?

(a)150 km/h and 105 km/h
(b)180 km/h and 108 km/h
(c)150 km/h and 250 km/h
(d)160 km/h and 106 km/h

Answer

Why

Correct — B. Crossing means covering both lengths: 150 + 250 = 400 m.

Same direction, 20 s: 400 ⁄ 20 = 20 m/s = u − v
Opposite directions, 5 s: 400 ⁄ 5 = 80 m/s = u + v

Add the two: 2u = 100 → u = 50 m/s
Subtract: 2v = 60 → v = 30 m/s

Convert with × 18⁄5:
50 m/s = 180 km/h, 30 m/s = 108 km/h → option (b)

Why the others are wrong

(a)
150 km/h and 105 km/h — 150 and 105 satisfy neither condition. The pair must add to 288 km/h and differ by 72 km/h, and 150 + 105 = 255. The 150 echoes a train length, which is a distance.
(c)
150 km/h and 250 km/h — 150 and 250 are the two lengths in metres reprinted as speeds. They add to 400 km/h, nowhere near the 288 km/h that a 400 m crossing in 5 seconds forces.
(d)
160 km/h and 106 km/h — 160 and 106 add to 266 km/h rather than 288 km/h. Testing the sum against the opposite-direction crossing kills this option in a single step, before any subtraction is needed.

Concept

When two trains cross each other the distance covered is the sum of their lengths, in either direction. Only the relative speed changes.

Same direction: relative speed = u − v. Opposite directions: relative speed = u + v. Two crossing times therefore give two linear equations in u and v, and adding and subtracting them beats substitution.

Stay in m/s while the lengths are in metres and convert only at the end: 1 m/s = 18⁄5 km/h.

The stem never says which train is faster, and the options are unordered pairs, so u is simply the larger of the two speeds. The lengths are not matched to the speeds anywhere.

Key facts

Two trains crossing each other cover the sum of their lengths, here 400 m.
Relative speed is u − v in the same direction and u + v in opposite directions.
1 m/s = 18⁄5 km/h, so 50 m/s is 180 km/h and 30 m/s is 108 km/h.

Study next

A train crossing a pole, where the distance is its own length aloneA train crossing a platform, where the distance is train length plus platform lengthBoats and streams, which reuse the same u + v and u − v pair with a current

Common traps

Using one train's length as the crossing distance instead of the sum.
Swapping the cases, so the 5-second crossing is treated as the same-direction one.
Converting with 5⁄18 instead of 18⁄5 when moving from m/s to km/h.

SSC either gives both crossing times and asks for the speeds, or gives both speeds and asks for a time — also asked 24 Sep 2024, 12:30, Quant Q.5, where goods trains of 132 m and 108 m approach each other at 32 km/h and 40 km/h.

Related PYQs

No directly related past PYQ was found.