SSC CGL 2024 Tier-I · 10 September 2024, Shift 1 · Quantitative Aptitude · Question 10 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.

Three pipes P, Q and R can fill a cistern in 40 minutes, 80 minutes and 120 minutes, respectively. Initially, all the pipes are opened. After how much time (in minutes) should the pipes Q and R be turned off so that the cistern will be completely filled in just half an hour?

(a)12
(b)16
(c)14
(d)10

Answer

Why

Correct — A. Take the cistern as 240 units (the LCM of 40, 80 and 120).

Rates: P = 240⁄40 = 6 units/min, Q = 240⁄80 = 3, R = 240⁄120 = 2.

P is never closed, so across the full half hour it delivers 6 × 30 = 180 units.
The tank still needs 240 − 180 = 60 units, and only Q and R can supply them.

Q and R together run at 3 + 2 = 5 units/min.
60 ÷ 5 = 12 minutes → option (a).

Why the others are wrong

(b)
16 — 16 minutes of Q and R adds 5 × 16 = 80 units to P's 180, giving 260 against a capacity of 240. The cistern would overflow before the half hour was up.
(c)
14 — 14 minutes supplies 5 × 14 = 70 units, ten more than the 60 the tank still lacks after P's contribution. The tank fills early, not in exactly 30 minutes.
(d)
10 — 10 is 60 ÷ 6 — the shortfall divided by P's rate instead of by Q and R's combined 5 units/min. It leaves the cistern 10 units short at the 30-minute mark.

Concept

Pipe questions turn into plain arithmetic once you replace "time to fill" with a rate. Give the cistern a convenient capacity — the LCM of the three filling times — and every rate becomes a whole number of units per minute.

After that it is a stock balance. The pipe that is never closed contributes for the whole duration, whatever the tank still lacks is the job of the pipes that close early, and their combined rate converts that shortfall into a time.

The question turns off Q and R together, so both run for the same stretch and one unknown carries the whole problem. Had they closed at different moments you would need two unknowns and a second condition.

Key facts

Work rate = 1 ÷ time, so a pipe that fills in 40 minutes does 1⁄40 of the tank each minute.
Taking the LCM of 40, 80 and 120 as the capacity (240 units) makes the rates of P, Q and R 6, 3 and 2 whole units per minute.
Total work done is the sum, over each pipe, of its rate multiplied by the time it actually ran.
P alone for 30 minutes fills 180 of the 240 units, which is why only 60 units are left for Q and R.

Study next

Tanks with a leak or an outlet pipe, where one rate is negativeAlternate-hour filling, where two pipes take turns instead of running togetherEquating work done to capacity when pipes open and close at different moments

Common traps

Missing that "half an hour" is 30 minutes while every rate is per minute.
Dividing the leftover 60 units by P's rate rather than by Q and R's combined rate, which lands on 10.
Assuming Q and R are shut at different times, which the question does not say.

SSC opens and shuts pipes partway through the fill, then asks either for a closing time or for the total.

The same construction runs at 9 Sep 2024, 12:30, Quant Q.25, where pipe S is closed 15 minutes before the tank overflows, and at 18 Sep 2024, 12:30, Quant Q.13, where pipe A is closed after three hours and B carries on alone.

Related PYQs

No directly related past PYQ was found.