SSC CGL 2024 Tier-I · 23 September 2024, Shift 3 · Quantitative Aptitude · Question 9 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.

A boat covers a distance of 55 km downstream in 5 hours while it takes 11 hours to cover the same distance upstream. What is the speed of the boat?

(a)8 km/h
(b)11 km/h
(c)7 km/h
(d)9 km/h

Answer

Why

Correct — A. Convert both journeys to speeds before doing anything else.
Downstream speed = 55 ⁄ 5 = 11 km/h
Upstream speed = 55 ⁄ 11 = 5 km/h

Downstream is boat + stream and upstream is boat − stream, so the boat's own speed is the mean of the two:
(11 + 5) ⁄ 2 = 16 ⁄ 2 = 8 km/h → option (a)

Check: the stream is (11 − 5) ⁄ 2 = 3 km/h, and 8 + 3 = 11 downstream, 8 − 3 = 5 upstream.

Why the others are wrong

(b)
11 km/h — 11 km/h is the downstream speed, which is boat plus stream. It answers 55 ⁄ 5 and stops there, leaving the current's 3 km/h inside the figure.
(c)
7 km/h — 7 km/h would need the two speeds to average 7. Upstream is fixed at 55 ⁄ 11 = 5 and downstream at 55 ⁄ 5 = 11, and their mean is 8.
(d)
9 km/h — 9 km/h is not the mean of 11 and 5 — that is 8. Averaging the downstream and upstream speeds is the entire method here, so a value one above the mean has no route to it.

Concept

Boats and streams is two linear equations wearing a story. If b is the boat's speed in still water and s the stream's, then downstream = b + s and upstream = b − s.

Add the two and the stream cancels: b = (downstream + upstream) ⁄ 2. Subtract them and the boat cancels: s = (downstream − upstream) ⁄ 2.

The one discipline the topic demands is converting to speeds first. Times cannot be averaged the way speeds can, because the same distance is covered in different times.

The question says "the speed of the boat", not "in still water", and the downstream speed 11 km/h is on the option list. The standard reading of that phrase is the still-water speed, which is what the key takes.

Key facts

Downstream speed = boat speed + stream speed, upstream speed = boat speed − stream speed.
Boat speed in still water = (downstream speed + upstream speed) ⁄ 2.
Stream speed = (downstream speed − upstream speed) ⁄ 2, here (11 − 5) ⁄ 2 = 3 km/h.

Study next

Finding the stream speed when only the total round-trip time is givenGetting the boat-to-stream ratio from the two journey times without any distanceAverage speed over a full round trip, which is the harmonic mean and not 8 km/h here

Common traps

Averaging the two times, 5 h and 11 h, instead of the two speeds.
Answering 11 km/h because the phrase "speed of the boat" is read as the speed it was actually travelling downstream.

The two-journey setup recurs with the target moved off the boat. Stream speed from a round trip in 7 hours 30 minutes is asked the same day at 23 Sep 2024, 12:30, Quant Q.9, and the boat-to-stream ratio from 18-hour and 36-hour legs at 17 Sep 2024, 12:30, Quant Q.12.

Related PYQs

No directly related past PYQ was found.

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