SSC CGL 2024 Tier-I · 25 September 2024, Shift 3 · Quantitative Aptitude · Question 16 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.

Seema walks around a circular field at the rate of 3 rounds per hour, while Priya runs around it at the rate of 8 rounds per hour. They start in the same direction from the same point at 11:54 p.m. They shall first cross each other at:

(a)12:06 a.m.
(b)12:06 p.m.
(c)12:00 a.m.
(d)11:59 p.m.

Answer

Why

Correct — A. Same direction, so the gap closes at the difference of the two rates.

Relative speed = 8 − 3 = 5 rounds per hour
They first cross when Priya has gained exactly one full round
Time = 1⁄5 hour = 60⁄5 = 12 minutes

11:54 p.m. + 12 minutes = 12:06 a.m. → option (a).

Six of those twelve minutes run out the day, so the crossing falls just after midnight.

Why the others are wrong

(b)
12:06 p.m. — The clock reading is right and the meridiem is wrong. 11:54 p.m. is late night, so adding 12 minutes crosses midnight into a.m. — 12:06 p.m. is midday, twelve hours away.
(c)
12:00 a.m. — 12:00 a.m. is only 6 minutes after the start. One gained lap at a relative 5 rounds per hour takes 12 minutes, not 6 — midnight is the next round number on the clock, not a computed time.
(d)
11:59 p.m. — 11:59 p.m. is 5 minutes on, and 5 is the relative speed in rounds per hour, not a count of minutes. Convert before you add: 1⁄5 of an hour is 12 minutes.

Concept

On a closed loop two bodies going the same way approach each other at the difference of their speeds, and they cross whenever the faster has gained a whole lap.

Rates given in rounds per hour save you the track length altogether — the circumference cancels, so no distance is needed anywhere in the working.

The first crossing is the first whole lap gained: 1 ÷ 5 hour = 12 minutes. Everything after that is clock arithmetic, and the start time is placed six minutes before midnight on purpose.

11:54 p.m. is chosen so the answer lands just past midnight — the meridiem is as much the question as the arithmetic is.

Key facts

Same direction on a circular track: relative speed is the difference of the two speeds.
Opposite directions: relative speed is the sum of the two speeds.
At a relative 5 rounds per hour, one lap is gained in 1⁄5 hour, which is 12 minutes.
12:06 a.m. is six minutes after midnight, and so falls on the next day.

Study next

First crossing anywhere on a circular track versus first meeting back at the startConverting a rate in rounds per hour into a time per roundAdding minutes across midnight and the a.m. to p.m. changeover

Common traps

Adding the rates, 3 + 8 = 11, which is the opposite-direction case.
Finishing the arithmetic and marking 12:06 p.m. without checking the meridiem.
Confusing the first crossing with the first meeting at the starting point, which needs the LCM of the lap times.

The same setup is dressed in metres and seconds elsewhere — a same-direction meeting on a 1,635 m track at 9 Sep 2024, 12:30, Quant Q.17, and a first meeting back at the starting point, needing the LCM of the lap times, at 17 Sep 2024, 16:00, Quant Q.5. Rounds per hour is the version that needs no track length.

Related PYQs

No directly related past PYQ was found.