SSC CGL 2024 Tier-I · 25 September 2024, Shift 1 · Quantitative Aptitude · Question 17 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 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.

An inlet pipe can fill a water storage tank in 11 hours and an outlet pipe can empty the completely filled tank in 15 hours .If both pipes opened simultaneously. The time taken to fill the empty tank ( in hrs) is :

(a)40
(b)
(c)
(d)

Answer

Why

Correct — B. Work in rates per hour and give the outlet a minus sign, because it takes water out.

Inlet rate = 1⁄11 tank per hour
Outlet rate = −1⁄15 tank per hour
Net rate = 1⁄11 − 1⁄15 = (15 − 11)⁄165 = 4⁄165 tank per hour
Time = 1 ÷ 4⁄165 = 165⁄4 = 41.25 = 41¼ hours

Option (b) is the picture showing 41¼.

The same sum in units: call the tank 165 units, the LCM of 11 and 15. The inlet brings in 15 units an hour, the outlet removes 11, so 4 units go in each hour and 165 ÷ 4 = 41.25 hours.

Why the others are wrong

(a)
40 — 40 is the plain-text option and it falls short. In 40 hours the pair moves 40 × 4⁄165 = 160⁄165 of the tank — close, but the tank is not yet full.
(c)
Option (c) shows 49¾. Run it forward: 49.75 × 4⁄165 = 1.21 tanks, so the tank would have overflowed well before then.
(d)
Option (d) shows 45½. At the net rate that fills 45.5 × 4⁄165 = 1.10 tanks — again past full, because it assumes a slower net inflow than 4⁄165.

Concept

Rates add; times do not. A pipe that fills in T hours works at 1⁄T of a tank per hour, and an outlet that empties in T hours works at −1⁄T.

Open both and the net rate is the sum of the signed rates: 1⁄11 − 1⁄15 = 4⁄165 of a tank each hour.

The filling time is the reciprocal of that net rate, 165⁄4 = 41¼ hours.

The sign matters more than the arithmetic. If the outlet were the faster pipe the net rate would be negative and an empty tank would never fill at all — which is why the direction of each pipe must be read before any numbers are written down.

The answer is a mixed fraction, 41¼, not a decimal.

A candidate who computes 41.25 and scans for 41.25 in the options can lose the mark to a formatting mismatch, so convert the quarter before matching.

Key facts

A pipe that fills a tank in T hours works at 1⁄T of the tank per hour.
An outlet that empties a full tank in T hours works at −1⁄T of the tank per hour.
Here the net rate is 1⁄11 − 1⁄15 = 4⁄165 of the tank per hour.
Filling time is the reciprocal of the net rate: 165⁄4 = 41.25 hours, which is 41¼ hours.

Study next

Fill-and-leak problems where the leak is discovered only after the tank fails to fill on timeThree-pipe problems with one outlet, handled by taking the tank as the LCM of the timesTime-and-work questions where one worker leaves partway through the job

Common traps

Adding the rates instead of subtracting, which gives 26⁄165 and about 6.35 hours
Subtracting the times themselves and answering 15 − 11 = 4 hours
Writing 165⁄4 as 41.4 hours instead of 41.25

SSC keeps this build to one inlet against one outlet and prints the answer as a mixed fraction, so the working has to be converted before it matches an option.

The leak version is asked 9 Sep 2024, 16:00, Quant Q.23, where a 12-hour pipe takes 18 hours because of a leak. Two-inlet builds appear at 19 Sep 2024, 16:00, Quant Q.1 and 26 Sep 2024, 09:00, Quant Q.21.

Related PYQs

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