SSC CGL 2024 Tier-I · 12 September 2024, Shift 1 · Quantitative Aptitude · Question 6 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 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.

M and N walk along a circular track. They start at 5:00 a.m. from the same point in the opposite directions. M and N walk at a speed of 5 rounds per hour and 2 rounds per hour, respectively. How many times will they cross each other before 6.30 a.m. on the same day?

(a)3
(b)7
(c)10
(d)5

Answer

Why

Correct — C. They move in opposite directions on a closed loop, so their speeds add.

Relative speed = 5 + 2 = 7 rounds per hour
Window 5:00 a.m. to 6:30 a.m. = 1.5 hours
Crossings = 7 × 1.5 = 10.5

A crossing is a whole event, so 10 of them have happened.

The 10th falls at 10 ÷ 7 hour = 85.7 minutes after 5:00, about 6:25:43.
The 11th would need 11 ÷ 7 hour = 94.3 minutes, which is past 6:30.

So they cross 10 times — option (c).

Why the others are wrong

(a)
3 — 3 is 5 − 2, the relative speed for walkers moving in the same direction. The question says opposite directions, where the speeds add to 7.
(b)
7 — 7 is the count for one hour. The window runs to 6:30, an hour and a half, so 7 must be multiplied by 1.5.
(d)
5 — 5 is M's own lap rate of 5 rounds per hour. Laps and crossings are different events, and at 7 rounds per hour of relative motion they meet every 8.6 minutes.

Concept

On a closed track, two walkers moving in opposite directions close the gap at the sum of their speeds; moving in the same direction, at the difference.

Speeds given in rounds per hour make the count immediate: one crossing happens for every complete round of relative motion, so crossings = relative speed × time.

The fractional part is discarded, not rounded. 10.5 means the eleventh meeting is only halfway to happening when the clock reaches 6:30.

Their common start at 5:00 is not counted as a crossing, and no crossing is double-counted at the start point.

Key facts

Opposite directions on a circular track: relative speed is the sum of the two speeds.
Same direction: relative speed is the difference of the two speeds.
Number of meetings in a period = relative speed in rounds per unit time × time, whole-number part only.
At 7 rounds per hour of relative motion M and N meet every 60/7 minutes, about 8 minutes 34 seconds.

Study next

Meetings at the starting point, which need the LCM of the two lap times rather than the relative speedCircular-track items given in metres per second with a stated track lengthSame-direction overtaking counts and how they differ from crossings

Common traps

Adding the speeds for same-direction motion and subtracting them for opposite directions
Using one hour when the window is 5:00 to 6:30
Rounding 10.5 up to 11 when the eleventh crossing falls after the deadline

SSC varies the direction and the units between shifts but keeps the relative-speed step.

Also asked 13 Sep 2024, 12:30, Quant Q.5 (opposite directions, 10 m/s and 8 m/s on a 1620 m track) and 26 Sep 2024, 09:00, Quant Q.15 (same direction, 220 m track).

The near-miss to watch is 17 Sep 2024, 16:00, Quant Q.5 — lap times of 180 s and 420 s, but it asks when they next meet at the starting point, which is LCM(180, 420) and not a crossing count.

Related PYQs

No directly related past PYQ was found.