SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 4 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.

A policeman noticed a thief at a distance of 500 metres. The policeman started running and the thief also started running at the same time. The thief is running at a speed of 15 km/h. It took 15 minutes for the policeman to catch the thief. Find the speed of the policeman (in km/h).

(a)10
(b)17
(c)11
(d)12

Answer

Why

Correct — B. The policeman does not cover 500 m in 15 minutes; he gains 500 m on a thief who keeps running.

Gap to close = 500 m = 0.5 km
Time = 15 min = 15 ⁄ 60 = 0.25 h
Relative speed = 0.5 ⁄ 0.25 = 2 km/h

Same direction, so relative speed = policeman − thief
Policeman = 15 + 2 = 17 km/h → option (b)

Why the others are wrong

(a)
10 — 10 km/h is slower than the thief's 15 km/h, so the gap widens instead of closing and no catch ever happens.
(c)
11 — 11 km/h is also below the thief's 15 km/h; any speed under 15 loses ground, so the whole option can be rejected on sight.
(d)
12 — 12 km/h gives a relative speed of −3 km/h, meaning the policeman falls a further 750 m behind during those 15 minutes.

Concept

In a chase, only the relative speed matters. When two bodies move in the same direction the relative speed is the difference of their speeds; when they move towards each other it is the sum.

The time to close a gap is therefore gap ÷ relative speed. Rearranged, relative speed = gap ÷ time, which is the step that produces the 2 km/h here.

The final line is the one candidates skip: 2 km/h is the excess, not the policeman's speed. Add the thief's 15 km/h back.

Units are mixed on purpose — metres in the gap, minutes in the time, km/h in the options — so convert before dividing.

Key facts

Same direction: relative speed is the difference of the two speeds.
Opposite directions: relative speed is the sum of the two speeds.
Closing time = initial gap ÷ relative speed, with both in the same units.
500 m = 0.5 km and 15 minutes = 0.25 hour.

Study next

Chase problems where the head start is given in time rather than distanceTrain-crossing problems solved as relative-speed itemsBoats and streams, where the stream speed is added or subtracted the same way

Common traps

Answering 2 km/h — the relative speed — instead of the policeman's own speed.
Dividing 500 by 0.25 with the gap still in metres.
Adding the two speeds, which applies only when the runners move towards each other.

The same shift's Quant Q.24 strips the story away and tests both cases at once: two cars 20 km apart on a highway meet in one hour going the same way and in 12 minutes going towards each other.

Related PYQs

No directly related past PYQ was found.