SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 12 of 99

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.

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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.

In a circular race of 4800m, A and B start from the same point and at the same time with speeds of 36 km/h and 54 km/h. When will they meet again for the first time on the track if they are running in the opposite direction?

(a)200 second
(b)205 second
(c)192 second
(d)178 second

Answer

Why

Correct — C. Opposite directions on a closed loop means the gap between the two runners closes at the sum of their speeds.

36 km/h = 36 × 5⁄18 = 10 m/s
54 km/h = 54 × 5⁄18 = 15 m/s
Relative speed = 10 + 15 = 25 m/s

They meet again once they have together covered one full lap of 4800 m:
time = 4800 ÷ 25 = 192 seconds → option (c).

Why the others are wrong

(a)
200 second — 200 s needs a closing speed of 4800 ÷ 200 = 24 m/s. Neither 10 m/s, nor 15 m/s, nor their sum of 25 m/s produces 24.
(b)
205 second — 205 s implies 4800 ÷ 205 ≈ 23.4 m/s. The pair close at exactly 25 m/s, so the first meeting cannot come later than 192 s.
(d)
178 second — 178 s implies about 27 m/s, faster than the true closing speed of 25 m/s. The error here is too quick, not too slow.

Concept

On a circular track two runners who start together meet again when the distance between them, measured along the track, has changed by one full lap.

Opposite directions: they approach, so the closing speed is the sum, and the first meeting comes after track length ÷ (u + v).

Same direction: one gains on the other, so use the difference, and the first meeting comes after track length ÷ (u − v). That would be 4800 ÷ 5 = 960 s here, five times as long.

Meet again for the first time means anywhere on the track, so you need one lap of relative distance. Meeting again at the starting point is a different question: that is the LCM of the two lap times, 480 s and 320 s, which is 960 s.

Key facts

To convert km/h into m/s multiply by 5⁄18, so 36 km/h = 10 m/s and 54 km/h = 15 m/s.
Running in opposite directions on a circular track, two runners first meet after (track length) ÷ (sum of speeds).
Running in the same direction they first meet after (track length) ÷ (difference of speeds).
One lap takes the slower runner 480 s and the faster runner 320 s on this 4800 m track.

Study next

Circular-track meetings: sum of speeds against difference of speedsFirst meeting anywhere on the track against first meeting at the starting pointConverting km/h into m/s before pairing a speed with a distance in metres

Common traps

Subtracting the speeds, which answers the same-direction version and gives 960 s.
Dividing 4800 by 90 without converting km/h into m/s, mixing metres with kilometres.
Reading meet again as returning together to the start, which is the LCM of the lap times.

The same set-up returns at 26 Sep 2024, 16:00, Quant Q.23, which asks for the opposite-direction and same-direction meeting times together on a 1600 m track. A rounds-per-hour variant, counting how often two walkers cross inside a fixed window, appears at 12 Sep 2024, 09:00, Quant Q.6.

Related PYQs

No directly related past PYQ was found.