SSC CGL 2024 Tier-I · 11 September 2024, Shift 1 · Quantitative Aptitude · Question 17 of 95

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.

There are two pipes to fill a tank. Together, they can fill the tank in 15 minutes. If one pipe can fill the tank in one and a half times as fast as the other, the faster pipe alone can fill the tank in:

Answer

Why

Correct — C. 'One and a half times as fast' compares rates, so put the rates in the ratio 3 : 2.

Let the slower pipe's rate be 2u and the faster pipe's 3u
Together they fill 1 tank in 15 minutes: 2u + 3u = 5u = 1⁄15 tank per minute
So u = 1⁄75
Faster pipe's rate = 3u = 3⁄75 = 1⁄25 tank per minute

A rate of 1⁄25 per minute means the faster pipe alone fills it in 25 minutes → option (c), the image reading '25 minutes'.

Check: the slower pipe is 2u = 1⁄37.5, and 1⁄25 + 1⁄37.5 = 1⁄15.

Why the others are wrong

(a)
Option (a) reads 10 minutes, less than the 15 the two pipes need together. One pipe alone can never beat both pipes running at once.
(b)
Option (b) reads 20 minutes. That makes the slower pipe 30 minutes, and 1⁄20 + 1⁄30 = 1⁄12 — the tank would fill in 12 minutes, not 15.
(d)
Option (d) reads 32½ minutes. Treat that as the faster pipe and the slower becomes 48¾, which together fill the tank in 19½ minutes, not 15.

Concept

Work questions are rate questions. A pipe that fills a tank in t minutes works at 1⁄t tank per minute, and rates add when pipes run together.

'One and a half times as fast' compares those rates: r_fast = 1.5 × r_slow. The alone-times then come out in the inverse ratio, 2 : 3 — the faster pipe 25 minutes, the slower 37½.

The check never changes: the two individual rates must add back to 1⁄15.

All four options are printed as images: (a) 10 minutes, (b) 20 minutes, (c) 25 minutes and (d) 32½ minutes.

Reading the comparison the other way — 'takes one and a half times as long' — produces the same pair of times, 25 and 37½, but hands the label 'faster' to 37½, which is not on the list.

Key facts

A pipe filling a tank in t minutes has rate 1⁄t, and rates add when pipes run together.
If one pipe is k times as fast as another, their alone-times are in the ratio 1 : k.
1⁄25 + 1⁄37.5 = 1⁄15, so 25 and 37½ minutes are the two pipes' times.
Either pipe alone must take longer than the 15 minutes the pair takes together.

Study next

Pipes and cisterns where an outlet pipe subtracts from the combined rateTurning 'k times as fast' into a ratio of timesTwo workers with a known rate ratio and a given combined time

Common traps

Reading it as 'takes one and a half times as long', which names 37½ minutes as the faster pipe.
Dividing 15 by 1.5 to get 10, a time quicker than both pipes together.
Answering with the slower pipe's 37½ minutes when the faster one is asked for.

The template repeats almost word for word at 13 Sep 2024, 09:00, Quant Q.7 — together in 20 minutes, one pipe 'two and a half times as quickly', faster pipe alone — and its key is 28 minutes, which is what the rate reading gives.

The same 'times as fast' wording drives 26 Sep 2024, 09:00, Quant Q.21 (four times as fast, together in 48 minutes, slower pipe asked, key 240). The same idea in a different sentence shape is at 26 Sep 2024, 16:00, Quant Q.7 (B twice as fast as A, together in 45 minutes, key 135).

Related PYQs

No directly related past PYQ was found.