SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 12 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.

The speed of a boat in still water is 18 km/h and the speed of the stream is 3 km/h. How much time (in hours) will it take to cover a distance of 105 km in downstream and in coming back?

(a)12
(b)10
(c)9
(d)15

Answer

Why

Correct — A. Find the two speeds, then time each leg separately.

Downstream speed = 18 + 3 = 21 km/h
Upstream speed = 18 − 3 = 15 km/h

Time downstream = 105 ÷ 21 = 5 h
Time upstream = 105 ÷ 15 = 7 h

Total = 5 + 7 = 12 hours → option (a)

Why the others are wrong

(b)
10 — 10 is 210 ÷ 21, the whole round trip run at the downstream speed. The return leg is against the stream at 15 km/h, so it cannot also take 5 hours.
(c)
9 — 9 is impossible before any working: 210 km in 9 hours needs an average of about 23.3 km/h, faster than the boat's best speed of 21 km/h downstream.
(d)
15 — 15 is the upstream speed in km/h, not a time. It also fails a sanity check — 210 km in 15 hours averages 14 km/h, slower than the slower leg.

Concept

In stream problems the boat's own speed and the current add going downstream and subtract going upstream: b + s and b − s.

Time is distance ÷ speed on each leg separately. You cannot average the two speeds and divide once, because the boat spends unequal amounts of time at each speed.

Here 18 and 3 give 21 and 15, and 105 divides cleanly by both — the numbers were chosen so each leg is a whole number of hours.

The round-trip average works out at 210 ÷ 12 = 17.5 km/h, not 18. That is the harmonic mean of 21 and 15, and it is always below the still-water speed.

Key facts

Downstream speed is boat speed plus stream speed, here 18 + 3 = 21 km/h.
Upstream speed is boat speed minus stream speed, here 18 − 3 = 15 km/h.
A there-and-back average speed is the harmonic mean of the two leg speeds, here 17.5 km/h.

Study next

Recovering boat and stream speeds from given upstream and downstream timesHarmonic mean as the average speed of a there-and-back journeyProblems where the return distance differs from the outward distance

Common traps

Averaging 21 and 15 to 18 and dividing 210 by it in one step
Reading the 105 km as the round-trip distance rather than one leg
Answering 15 because the upstream speed appears in the option list as a number

The item is one step deep and is decided entirely by whether you split the journey into two legs with different speeds.

The same 'work out each rate, then combine' habit is tested on pipes at Quant Q.14 of this shift.

Related PYQs

No directly related past PYQ was found.