SSC CGL 2024 Tier-I · 13 September 2024, Shift 3 · Quantitative Aptitude · Question 17 of 98

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.

Two pipes P and Q can fill a tank in 36 minutes and 45 minutes, respectively. If both pipes are opened together, the time taken to fill the tank is:

(a)10 minutes
(b)40.5 minutes
(c)20 minutes
(d)81 minutes

Answer

Why

Correct — C. Add the rates, never the times.

P fills 1⁄36 of the tank per minute
Q fills 1⁄45 per minute

Take the LCM of 36 and 45, which is 180:
1⁄36 + 1⁄45 = 5⁄180 + 4⁄180 = 9⁄180 = 1⁄20 per minute

A rate of one-twentieth of the tank each minute empties into 20 minutes for the whole tank → option (c).

Why the others are wrong

(a)
10 minutes — 10 minutes is below 18, and two pipes can never beat half the faster pipe's own time — half of 36 is 18. This one is ruled out before any arithmetic.
(b)
40.5 minutes — 40.5 is the average of 36 and 45. Two pipes working together must finish sooner than the faster of them, so any figure above 36 is wrong on sight.
(d)
81 minutes — 81 is 36 + 45. Times add only when pipes run one after the other; running together, it is their rates that add.

Concept

Work-rate problems convert a time into a rate: a pipe that fills a tank in t minutes fills 1⁄t of it each minute.

Rates add when the pipes run at once, which is why the combined rate is 1⁄36 + 1⁄45 = 1⁄20 and the combined time is its reciprocal, 20 minutes.

For exactly two filling pipes this collapses to t₁t₂⁄(t₁ + t₂) = 36 × 45 ÷ 81 = 20, which is faster than finding an LCM under exam pressure.

Two bounds make the arithmetic self-checking: the answer must be less than 36 and more than 18.

The four options are placed so that each wrong one names a specific slip: the average, the sum, and a value below the lower bound. Nothing here is a near-miss of the real arithmetic.

Key facts

A pipe filling a tank in t minutes contributes a rate of 1⁄t per minute.
For two filling pipes the combined time is t₁t₂ ÷ (t₁ + t₂), here 36 × 45 ÷ 81 = 20 minutes.
Rates add when pipes run together, while times add only when they run one after the other.
The combined time always lies between half the faster time and the faster time itself, so between 18 and 36 minutes here.

Study next

Three-pipe problems where an outlet pipe's rate is subtracted from the inletsPipes opened or closed part-way, where you total the work done in each stretchAlternate-hour filling, where a two-hour cycle becomes the unit of work

Common traps

Averaging the two times to reach 40.5
Adding the two times to reach 81
Treating the LCM, 180, as the answer rather than as a working step

The plain two-pipe opener returns with fresh numbers — also asked 10 Sep 2024, 12:30, Quant Q.7 (pipes of 30 and 45 hours) and 25 Sep 2024, 12:30, Quant Q.3 (pipes of 14 and 21 hours).

Harder versions bolt an outlet pipe or a mid-way closure onto the same rate sum, as on 12 Sep 2024, 12:30, Quant Q.14, where pipe B is shut early.

Related PYQs

No directly related past PYQ was found.