SSC CGL 2024 Tier-I · 18 September 2024, Shift 3 · Quantitative Aptitude · Question 2 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 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.

Pipe Q can fill the tank in 60 hours while pipe R may fill in 45 hours. Q and R pipes are opened together for 6 hours after which pipe W is also opened to empty the tank. All three pipes are opened simultaneously for 24 hours to reach the half level mark. How much time (in hours) will pipe W alone take to empty the entire tank?

(a)36
(b)48
(c)42
(d)30

Answer

Why

Correct — A. Take the tank as 180 units, the LCM of 60 and 45.

Q fills 180 ⁄ 60 = 3 units/h, R fills 180 ⁄ 45 = 4 units/h
Q and R together = 7 units/h
First 6 hours, Q and R only: 6 × 7 = 42 units

Half the tank is 90 units, so the next 24 hours must add 90 − 42 = 48 units
Net rate with W open = 48 ⁄ 24 = 2 units/h
W therefore drains 7 − 2 = 5 units/h

W alone on a full tank: 180 ⁄ 5 = 36 hours → option (a)

Why the others are wrong

(b)
48 — At 48 hours W drains 180 ⁄ 48 = 3.75 units/h, so the net becomes 3.25 units/h. Those 24 hours would carry the tank to two-thirds full, well past the half mark the question fixes.
(c)
42 — 42 hours puts W at 30⁄7 units/h and the net at 19⁄7 units/h. After the 24 hours the tank would stand at 25⁄42 full, again above half.
(d)
30 — 30 hours makes W drain 6 units/h, leaving a net of just 1 unit/h. The tank would reach only 11⁄30 of its capacity in the 24 hours, short of half.

Concept

Pipes-and-cisterns questions are rate addition, and the LCM unit method keeps them free of fractions.

Call the tank 180 units, the LCM of 60 and 45. Q then works at 3 units an hour and R at 4. An outlet counts as a negative rate, so with W open the net is 7 minus W's own rate.

The sentence "to reach the half level mark" fixes the work done, not the time. That is what converts the 24-hour stretch into 48 units and pins W's rate.

The question names the pipes Q, R and W rather than A, B and C, and gives the two filling times out of order.

Note also that the 6 hours and the 24 hours are consecutive, not overlapping: the tank holds 42 units when W opens, and 90 units when the 24 hours end.

Key facts

Taking the tank as the LCM of the given times gives every pipe a whole-number rate.
An emptying pipe carries a negative rate, so the net rate is the fills minus the drains.
Q and R together move 7 of 180 units an hour, filling the tank in 180⁄7 hours on their own.
W drains 5 units an hour, which is 180 ⁄ 5 = 36 hours for a full tank.

Study next

The LCM unit method for pipes and cisternsNet rate when an outlet or leak runs alongside inletsTwo-stage tank problems where a pipe opens or closes partway through

Common traps

Reading "half level mark" as half the time rather than half the volume.
Forgetting that 42 units are already in the tank before W opens.
Reporting W's net effect of 2 units an hour instead of W's own 5 units an hour.

SSC likes the two-stage tank: one stretch with the inlets alone, then the outlet joins or leaves. A closing-outlet version is asked at 12 Sep 2024, 09:00, Quant Q.7, where pipe C is shut 2 minutes before the tank fills.

Related PYQs

No directly related past PYQ was found.