SSC CGL 2024 Tier-I · 26 September 2024, Shift 1 · Quantitative Aptitude · Question 15 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 athletes are participating in a race on a circular track of 220 m. Ravi runs at the speed of 22 m/s, while Kapil runs at the speed of 11 m/s. They start from the same point, at the same time and in the same direction. After how many seconds will they meet for the first time?

(a)15 seconds
(b)20 seconds
(c)16 seconds
(d)24 seconds

Answer

Why

Correct — B. Running the same way round, the gap closes at the difference of the speeds.

Relative speed = 22 − 11 = 11 m/s
To meet again, Ravi must gain a full lap on Kapil: 220 m
Time = 220 ⁄ 11 = 20 seconds → option (b)

Check: in 20 s Ravi covers 440 m (two laps) and Kapil 220 m (one lap), so both are at the same point.

Why the others are wrong

(a)
15 seconds — In 15 s Ravi gains 11 × 15 = 165 m, short of the 220 m lap he needs. At that instant they are 165 m apart along the track.
(c)
16 seconds — In 16 s the gain is 11 × 16 = 176 m, still inside one lap. A meeting needs the gain to reach 220 m exactly.
(d)
24 seconds — By 24 s the gain is 264 m, a lap plus 44 m — they have already met at 20 s and separated again, and the stem asks for the first meeting.

Concept

On a circular track, a meeting is decided by relative speed, not by either runner's own speed.

Same direction: the gap grows at the difference of the speeds, and the runners are together again when that gap equals one full circumference. Opposite directions: the gap closes at the sum, and one circumference between them is again the condition.

So the first meeting comes at track length ÷ relative speed — here 220 ÷ 11 = 20 s.

Key facts

Same direction: first meeting after track length ÷ (difference of speeds).
Opposite directions: first meeting after track length ÷ (sum of speeds) — 220 ⁄ 33 s for these two.
Ravi's lap takes 220 ⁄ 22 = 10 s and Kapil's takes 220 ⁄ 11 = 20 s.
Meeting back at the starting point takes the LCM of the lap times, 20 s, which agrees here.

Study next

Opposite-direction meetings on a circular trackMeetings at the starting point via the LCM of individual lap timesThree-runner circular track problems and their first common meeting

Common traps

Adding the speeds, 22 + 11 = 33, as though the runners went opposite ways.
Dividing the track length by the faster runner's speed alone, which gives 10 s.
Confusing 'meet anywhere on the track' with 'meet at the starting point' — that second one is the LCM of the lap times, which happens to be 20 s here too.

The stem gives a track length and two speeds and asks for a first meeting. Subtract the speeds for the same direction, add them for opposite, then divide the length by the result.

Related PYQs

No directly related past PYQ was found.