SSC CGL 2024 Tier-I · 9 September 2024, Shift 1 · Quantitative Aptitude · Question 3 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 6 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.

In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?

(a)140 s
(b)40 s
(c)70 s
(d)20 s

Answer

Why

Correct — A. Runners going the same way round a circular track meet again when the faster one has gained a full lap on the slower.

Relative speed = 12 − 6 = 6 m/s.
Ground to be gained = one lap = 840 m.

Time = distance ÷ relative speed
= 840 ⁄ 6 = 140 s → option (a).

Why the others are wrong

(b)
40 s — In 40 s the faster runner gains only 6 × 40 = 240 m, far short of the 840 m lap he must make up before they meet.
(c)
70 s — 70 s is 840 ⁄ 12, the time B needs for one lap of his own. A lap of the track is not a lap gained on A, who has himself covered 420 m in that time.
(d)
20 s — 20 s opens a gap of just 120 m. Even the opposite-direction formula, 840 ⁄ (12 + 6) ≈ 46.7 s, does not produce 20.

Concept

On a circular track the runners meet again when the gap between them equals one whole lap, not zero.

Same direction: subtract the speeds. Opposite directions: add them.

Time to meet = circumference ⁄ relative speed, which here is 840 ⁄ (12 − 6) = 140 s.

Meeting again at the starting point is a different question and needs the LCM of the two individual lap times.

The question asks when they meet next anywhere on the track. On these numbers the lap times are 140 s and 70 s, so the first meeting at the starting point also falls at 140 s — the two versions happen to coincide.

Key facts

Same direction on a circular track: time to meet = circumference ÷ (difference of the speeds).
Opposite directions: time to meet = circumference ÷ (sum of the speeds).
Here 840 ÷ (12 − 6) = 140 seconds.

Study next

Meeting at the starting point, which uses the LCM of the individual lap timesThree runners on one track and the first instant all three coincideCounting the distinct meeting points on a circular track from the ratio of the speeds

Common traps

Adding the speeds out of habit, which is the opposite-direction case
Dividing the track by the faster runner's speed, which gives his own lap time of 70 s

The numbers are built so the lap divides the speed difference exactly, 840 ⁄ 6, leaving one division once the same-direction rule has been picked.

Related PYQs

No directly related past PYQ was found.