SSC CGL 2024 Tier-I · 25 September 2024, Shift 2 · Quantitative Aptitude · Question 7 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 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.

A policeman noticed a thief at some distance. The policeman started running to catch the thief and the thief also started running at the same time. The speed of both policeman and the thief was 12 km per hour and 10 km per hour, respectively. It took 30 minutes for the policeman to catch the thief. Find the initial distance (in metres) between them.

(a)1000
(b)600
(c)100
(d)500

Answer

Why

Correct — A. A chase closes the gap at the difference of the two speeds, not at either speed.

Relative speed = 12 − 10 = 2 km/h
Time = 30 minutes = 1⁄2 hour

Gap closed = 2 × 1⁄2 = 1 km

The catch happens exactly when the gap closed equals the head start, so the initial distance is 1 km = 1,000 metres → option (a)

Why the others are wrong

(b)
600 — 600 m is the ground the policeman gains in 18 minutes at 2 km/h, not in 30. The chase runs for half an hour, and 2 × 1⁄2 = 1 km.
(c)
100 — 100 m is out by a factor of ten, the slip that comes from writing 1 km as 100 m. A kilometre is 1,000 metres.
(d)
500 — 500 m is what you get from half the relative speed, or from reading the 30 minutes as 15. At 2 km/h the gap closes by a full kilometre in half an hour.

Concept

Two bodies moving in the same direction approach each other at the difference of their speeds. Moving towards each other, they approach at the sum.

Both run the same way here, so the policeman gains 12 − 10 = 2 km every hour, no matter how much ground either has covered.

Catching up means the gain equals the head start, so initial distance = relative speed × time.

The unit switch is the other half of the question. Minutes must become hours before you multiply by a speed in km/h, and the answer has to come back in metres.

The paper never states that the two run in the same direction — the word chase carries it. The stem also gives speeds in km/h while asking for metres, so the conversion is part of the question rather than an afterthought.

Key facts

Same-direction relative speed is the difference of the speeds, opposite-direction is the sum.
In a catch-up chase the initial gap equals relative speed multiplied by the time taken to catch.
30 minutes is 1⁄2 hour, and 2 km/h × 1⁄2 h = 1 km = 1,000 m.

Study next

Chase problems that give the head start and ask for the time to catchRelative speed for two trains crossing in the same and in opposite directionsConverting km/h to m/s with the factor 5⁄18

Common traps

Using 12 km/h alone, which gives 6 km and ignores that the thief is also running
Leaving the 30 in minutes and multiplying it by a speed quoted in km/h
Answering in kilometres when the stem asks for metres

SSC runs this stem in both directions. Here the time is given and the gap is wanted; at 23 Sep 2024, 09:00, Quant Q.2 a 92 m gap is given and the time is wanted, and at 24 Sep 2024, 16:00, Quant Q.10 a 1,300 m gap with speeds of 82 and 64 km/h is asked in seconds.

Related PYQs

No directly related past PYQ was found.