SSC CGL 2024 Tier-I · 19 September 2024, Shift 3 · Quantitative Aptitude · Question 1 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.

Two inlet pipes, P1 and P2, can fill a cistern in 20 hours and 30 hours, respectively. They were opened at the same time, but pipe P1 had to be closed 5 hours before the cistern was full. How many hours in total did it take for the two pipes to fill the cistern?

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

Answer

Why

Correct — A. Take the cistern as 60 units, the LCM of 20 and 30, so P1 fills 3 units an hour and P2 fills 2 units an hour.

P2 runs for the whole time T. P1 runs only T − 5, because it is closed 5 hours before the cistern is full.

3(T − 5) + 2T = 60
5T − 15 = 60
T = 75⁄5 = 15 hours → option (a).

Check: P1 works 10 h (30 units), P2 works 15 h (30 units), and 30 + 30 = 60.

Why the others are wrong

(b)
9 hours — 9 hours leaves the cistern half empty. P1 would run 4 hours (4⁄20 = 1⁄5) and P2 the full 9 (9⁄30 = 3⁄10), and 1⁄5 + 3⁄10 is only half the job.
(c)
12 hours — 12 hours answers a different question — the time if both pipes ran throughout. With P1 shut for the last 5 hours you reach 7⁄20 + 12⁄30 = 3⁄4 of the cistern.
(d)
10 hours — 10 hours is how long P1 actually runs in the correct solution, not the total elapsed time. At 10 hours the cistern is 5⁄20 + 10⁄30 = 7⁄12 full.

Concept

Pipe-and-cistern sums are rate sums. Turn each filling time into a rate, most cleanly by taking the cistern as the LCM of the given times so that every rate is a whole number of units an hour.

Then write one equation in the total time T, giving each pipe the hours it is actually open. The phrase "closed 5 hours before the cistern was full" fixes P1's running time at T − 5, not at 5. Those last 5 hours belong to the end of the job, when P2 works alone.

The options are all measured in total elapsed time, so T is what you must report — not the time either pipe was open.

Key facts

Taking the cistern as the LCM of the filling times (here 60 units) turns both rates into whole numbers.
P1 fills 3 units an hour and P2 fills 2, so together they fill 5 units an hour.
"Closed 5 hours before the tank is full" means that pipe runs for T − 5 hours, where T is the total time.
The answer must exceed 12 hours, the both-pipes-throughout time, because part of the work is left to P2 alone.

Study next

Tanks with a leak, where the emptying pipe enters the same equation with a negative rateAlternate-opening problems, in which pipes are run in turns of an hour or twoWork-and-wages sums, which use the identical rate equation with workers in place of pipes

Common traps

Reading "closed 5 hours before the end" as "closed after 5 hours", which gives 22.5 hours
Reporting P1's running time of 10 hours instead of the total 15
Forgetting that P2 alone finishes the job, so the answer must be longer than the 12 hours both pipes would need

SSC sets the plain version — both pipes open throughout — at 10 Sep 2024, 12:30, Quant Q.7, where pipes of 30 and 45 hours are opened together.

The harder variants change what happens partway through the job, as at 17 Sep 2024, 12:30, Quant Q.25, where an obstruction cuts both flows for part of the filling.

Related PYQs

No directly related past PYQ was found.