SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 15 of 95

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

We doubt SSC's key on this question.

After setting off, the three are together at the start only at 11:00 a.m. and 1:00 p.m., so option (b), 2 times, is equally defensible; the keyed 3 also counts the 9:00 a.m. start as a meeting, which the stem does not say, and this card follows the key.

The answer below is still the option SSC's key marks, and we solve to that option.

Three friends, X, Y, and Z, are cycling on a circular track with a circumference of 2 km. They all start from the same point at 9:00 a.m. and travel in the same direction with speeds of 10 km/h, 12 km/h, and 15 km/h respectively. How many times will all three of them meet at the starting point if they continue cycling until 1:00 p.m.?

(a)1 time
(b)2 times
(c)3 times
(d)4 times

Answer

Why

Correct — C.
Lap time = 2 km ÷ speed:
X = 2⁄10 h = 12 min, Y = 2⁄12 h = 10 min, Z = 2⁄15 h = 8 min

All three are at the start together every LCM(12, 10, 8) = 120 min = 2 hours.

Moments together at the start: 9:00 a.m., 11:00 a.m. and 1:00 p.m.
Counting the 9:00 start, as the key does, that is 3 times → option (c)

Why the others are wrong

(a)
1 time — 1 time counts only 11:00 a.m. It drops the 9:00 start and the 1:00 p.m. return, when X, Y and Z have done 20, 24 and 30 laps.
(b)
2 times — 2 times counts the returns at 11:00 a.m. and 1:00 p.m. but not the start. The key also counts 9:00 a.m., when all three stand at the point together.
(d)
4 times — 4 times needs another meeting, say at 10:00 a.m. But by 10:00 Z has ridden 60 ÷ 8 = 7.5 laps and is halfway round, so the three are not together.

Concept

On a circular track a rider is back at the start after every whole lap. All three are there together at a common multiple of their lap times, and the first such moment is the LCM.

So turn speeds into lap times first. LCM(12, 10, 8) = 120 minutes, and the answer is the count of 2-hour marks that fall between 9:00 a.m. and 1:00 p.m.

Both ends of the window matter. 1:00 p.m. is a meeting because 240 minutes is a whole number of laps for all three (20, 24 and 30), and the key counts the 9:00 a.m. start as well.

Key facts

Lap time = track length ÷ speed: 12, 10 and 8 minutes here.
Riders on a circular track are all at the start together every LCM of their lap times.
LCM(12, 10, 8) = 120 minutes, so after the 9:00 a.m. start the common returns fall at 11:00 a.m. and 1:00 p.m.

Study next

First meeting anywhere on the track: track length ÷ relative speedRiders moving in opposite directions on a circular trackLCM of fractions, for lap times given in hours

Common traps

Taking the LCM of the speeds, 60 km/h, instead of the LCM of the lap times.
Leaving out the 1:00 p.m. return, which falls exactly at the end of the window.

17 Sep 2024, 16:00, Quant Q.5 asks for the first such meeting with two runners: lap times of 180 and 420 seconds give an LCM of 1,260 seconds, the 21 minutes its key marks.

Related PYQs

No directly related past PYQ was found.

Topic: Time and distance — all 58 SSC CGL questions on it, every solved shift.