SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 14 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.

Pipes P and Q can completely fill a water tank in 10 hours and 15 hours, respectively. A pipe R can empty a tank filled completely with water in 12 hours. Initially, the tank is empty and only pipes P and Q are opened at 6 a.m. and pipe R is also opened at 9 a.m. By what time will the tank be completely filled?

(a)3 p.m.
(b)11 a.m.
(c)1 p.m.
(d)2 p.m.

Answer

Why

Correct — A. Take the tank as 60 units, the LCM of 10, 15 and 12.

P fills 60 ÷ 10 = 6 units/h
Q fills 60 ÷ 15 = 4 units/h
R empties 60 ÷ 12 = 5 units/h

From 6 a.m. to 9 a.m. only P and Q run:
3 × (6 + 4) = 30 units filled, 30 units left.

From 9 a.m. all three run: 6 + 4 − 5 = 5 units/h
30 ÷ 5 = 6 more hours

9 a.m. + 6 h = 3 p.m. → option (a)

Why the others are wrong

(b)
11 a.m. — 11 a.m. is only five hours in: 30 units from the first three hours plus 2 × 5 = 10 more, leaving the tank at 40 of 60 units — two-thirds full.
(c)
1 p.m. — 1 p.m. is seven hours in: 30 + 4 × 5 = 50 of 60 units. The last 10 units still need two more hours at the reduced three-pipe rate.
(d)
2 p.m. — 2 p.m. is the near miss at eight hours: 30 + 5 × 5 = 55 units. One full hour of the 5 units/h rate remains, which is why the tank fills an hour later.

Concept

Pipe problems become plain arithmetic once you replace 'a tank' with a unit count, normally the LCM of the given times.

A filling pipe contributes a positive rate, an emptying pipe a negative one, and the combined rate is their sum for as long as they run together.

When pipes start at different times, split the clock into stretches over which the rate is constant and settle each stretch separately. Here the stretches are 6–9 a.m. at 10 units/h and 9 a.m. onwards at 5 units/h.

R halves the progress but does not reverse it, since 6 + 4 − 5 is still positive. Had R been faster than P and Q together the net rate would be negative and the tank would never fill, so check the sign before dividing.

Key facts

With the tank set at 60 units, P gives 6 units/h, Q gives 4 units/h and R removes 5 units/h.
P and Q alone fill 30 of the 60 units in the three hours from 6 a.m. to 9 a.m.
After 9 a.m. the net rate is 6 + 4 − 5 = 5 units/h, so the remaining 30 units take 6 hours.

Study next

Fillings in which a pipe is opened or closed part way throughNet rates that turn negative, giving a tank that never fillsConverting an emptying pipe into a negative rate under the LCM method

Common traps

Running all three pipes from 6 a.m. and using a single rate instead of splitting the clock at 9 a.m.
Adding R's 5 units/h instead of subtracting it
Counting the final 6 hours from 6 a.m. rather than from 9 a.m., which lands on noon

The staggered start is the whole difficulty here: because the answer is a clock time, a mistake in the split shows up as a wrong hour rather than a wrong fraction.

The same 'find each rate, then combine' method is what settles the boat question at Quant Q.12 of this shift.

Related PYQs

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