SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 17 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 5 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.

Varun and Sandeep started for a car race from the same point, in the same direction and at the same time on a circular track of length 1635 m with the speeds of 90 km/h and 108 km/h, respectively. After how much time (in s) will they meet again for the first time?

(a)327
(b)325
(c)324
(d)326

Answer

Why

Correct — A. Running the same way round the track, they meet again when the faster has gained exactly one full lap — so work in relative speed.

Convert with the × 5⁄18 rule:
90 km/h = 25 m/s
108 km/h = 30 m/s
Relative speed = 30 − 25 = 5 m/s

Time to gain one lap = 1,635 ÷ 5 = 327 s → option (a).

Why the others are wrong

(b)
325 — In 325 s the gap opens by 5 × 325 = 1,625 m — ten metres short of a lap, so Sandeep has not yet caught Varun. 1,635 ÷ 5 divides exactly, leaving no rounding to hide behind.
(c)
324 — 324 s gives a gain of 1,620 m, fifteen metres short of the 1,635 m needed. All four options sit within three seconds of each other, so the division has to be done, not eyeballed.
(d)
326 — 326 s is the closest decoy: it gains 1,630 m, five metres short. It catches anyone who divides 1,635 by 5 carelessly or trims a second in the conversion.

Concept

On a circular track only the relative speed matters. Same direction: subtract the speeds. Opposite directions: add them.

The first meeting comes after one relative lap, so t = track length ÷ relative speed. Where on the track it happens is irrelevant to the question.

Convert km/h to m/s by multiplying by 5⁄18 before anything else, so that the length in metres and the speeds in metres per second are in the same units.

Here the first meeting also happens to fall at the starting point: in 327 s Varun covers 8,175 m (5 laps) and Sandeep 9,810 m (6 laps). That is a coincidence of these numbers, not a rule — meeting anywhere is length ÷ relative speed, while meeting at the start is the LCM of the two lap times.

Key facts

Multiply km/h by 5⁄18 for m/s: 90 km/h = 25 m/s and 108 km/h = 30 m/s.
Running the same way round the track, relative speed is the difference of the two speeds.
Running in opposite directions, relative speed is the sum.
First meeting on a circular track = track length ÷ relative speed = 1,635 ÷ 5 = 327 s.

Study next

Opposite-direction meetings on a circular track, where t = length ÷ sum of the speedsMeeting again at the starting point, from the LCM of the individual lap timesThree runners on one track: the LCM of the pairwise meeting times

Common traps

Adding the speeds as if they ran in opposite directions: 1,635 ÷ 55 ≈ 29.7 s
Skipping the 5⁄18 conversion and dividing 1,635 by the 18 km/h difference
Using one runner's own speed instead of the relative speed, which answers a lap time, not a meeting time

SSC keeps the numbers clean — speeds differing by a multiple of 18 km/h so the relative speed is a whole number of m/s, and a track length that divides exactly. Usually only the direction of running changes between shifts.

Related PYQs

No directly related past PYQ was found.