SSC CGL 2024 Tier-I · 18 September 2024, Shift 1 · Quantitative Aptitude · Question 19 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 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 motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed it can travel 32 km downstream and 12 km upstream in 10 hours. The speed of the stream is:

(a)5 km/h
(b)2 km/h
(c)3 km/h
(d)4 km/h

Answer

Why

Correct — C. Both conditions are linear in 1⁄speed, so substitute rather than solve for the speeds directly.

Let x = 1⁄(upstream speed) and y = 1⁄(downstream speed).
24x + 40y = 17
12x + 32y = 10, doubled → 24x + 64y = 20

Subtract the first from the doubled second: 24y = 3, so y = 1⁄8 and downstream speed = 8 km/h.

Back-substitute: 24x + 40⁄8 = 17 → 24x = 12 → x = 1⁄2, so upstream speed = 2 km/h.

Stream = (downstream − upstream)⁄2 = (8 − 2)⁄2 = 3 km/h → option (c).

Why the others are wrong

(a)
5 km/h — 5 km/h is the boat's own speed in still water, (8 + 2)⁄2, not the stream. The stream is the half-difference of the two speeds, not their half-sum.
(b)
2 km/h — 2 km/h is the upstream speed the working produces on the way to the answer. It is the boat fighting the current, not the current itself.
(d)
4 km/h — The equations fix the downstream speed at 8 km/h. A stream of 4 km/h would leave the boat at 4 km/h in still water and 0 km/h upstream, so it could never cover 24 km against the current.

Concept

For a boat of speed b in a stream of speed s, downstream = b + s and upstream = b − s.

Distances are given but times are shared, so the natural unknowns are the two composite speeds, not b and s. Treating 1⁄u and 1⁄v as the variables turns a pair of awkward fraction equations into a plain linear system.

Once u and v are known, s = (v − u)⁄2 and b = (v + u)⁄2.

The 24-and-40 line and the 12-and-32 line are chosen so that doubling the second makes the x-terms match. Spotting that saves you the elimination arithmetic entirely.

Key facts

Downstream speed = boat speed + stream speed, and upstream speed = boat speed − stream speed.
Stream speed is half the difference of the downstream and upstream speeds.
Here downstream = 8 km/h and upstream = 2 km/h, giving boat = 5 km/h and stream = 3 km/h.
Two distance-time conditions are enough to fix both composite speeds without ever naming b and s.

Study next

Boats and streams solved by substituting 1⁄upstream and 1⁄downstreamRecovering boat speed and stream speed from the half-sum and half-differenceTime-and-distance systems where the two equations share a common multiple

Common traps

Answering with the still-water speed when the question asks for the stream
Stopping at the reciprocal, so 1⁄8 or 1⁄2 is read as a speed
Adding the two speeds and halving, which returns the boat rather than the current

SSC sets this either as a two-equation system like this one, matched by 13 Sep 2024, 09:00, Quant Q.22, or as a single downstream-and-upstream pair to be split, as at 23 Sep 2024, 16:00, Quant Q.9.

Related PYQs

No directly related past PYQ was found.