SSC CGL 2025 Tier-I · 12 September 2025, Shift 1 · Quantitative Aptitude · Question 20 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 11 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.

Two cars, X and Y, start from points 360 km apart and travel at constant speeds. If they move towards each other, they meet in 4 hours. If they move in the same direction, they meet in 12 hours. What is the speed of car X? (Assume X is the faster car).

(a)60 km/h
(b)75 km/h
(c)45 km/h
(d)90 km/h

Answer

Why

Correct — A. Towards each other, the gap closes at the sum of the speeds. In the same direction it closes at the difference.

Sum: X + Y = 360 ÷ 4 = 90 km/h
Difference: X − Y = 360 ÷ 12 = 30 km/h

Add the two equations: 2X = 90 + 30 = 120
Halve it: X = 120 ÷ 2 = 60 km/h → option (a)

Check: Y = 90 − 60 = 30 km/h, and 60 − 30 = 30 ✓

Why the others are wrong

(b)
75 km/h — 75 km/h forces Y = 90 − 75 = 15 km/h. The gap would then close at 75 − 15 = 60 km/h, so the same-direction meeting takes 360 ÷ 60 = 6 hours, not 12.
(c)
45 km/h — 45 km/h is exactly half of 90, so Y would also be 45 km/h. Equal speeds in the same direction never close the gap, and the stem says X is faster.
(d)
90 km/h — 90 km/h is the sum of the two speeds — the closing speed when the cars drive towards each other. Taking it as X leaves Y at 0 km/h.

Concept

This is relative speed. Two objects moving towards each other close the gap at the sum of their speeds. Moving the same way, the faster one gains only at the difference.

Each meeting time gives one equation: gap ÷ time = relative speed. With the sum and the difference known, the faster speed is (sum + difference) ÷ 2 and the slower is (sum − difference) ÷ 2.

Here: (90 + 30) ÷ 2 = 60 and (90 − 30) ÷ 2 = 30.

For a same-direction meeting, the faster car X must start behind Y and chase it. The stem leaves this unstated, but if X started ahead the gap would only grow.

Key facts

Moving towards each other, relative speed = sum of the speeds.
Moving in the same direction, relative speed = difference of the speeds.
Faster speed = (sum + difference) ÷ 2, and slower speed = (sum − difference) ÷ 2.
Time to meet = starting gap ÷ relative speed.

Study next

Trains crossing on parallel tracks, where the two lengths make up the gapChase problems: a policeman and a thief starting some distance apartMeeting on a circular track in the same and in opposite directions

Common traps

Giving the sum of the speeds, 90 km/h, as X's speed.
Halving the sum, 90 ÷ 2 = 45, which assumes equal speeds and ignores the same-direction meeting.

The same sum-and-difference pair is on 10 Sep 2024, 12:30, Quant Q.24: cars 20 km apart meet in 1 hour going the same way and in 12 minutes head-on, so the speeds are 60 and 40 km/h.

Trains crossing on parallel lines use it on 19 Sep 2024, 09:00, Quant Q.21.

Related PYQs

No directly related past PYQ was found.

Topic: Time and distance — all 40 SSC CGL questions on it, every solved shift.