Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely ?

(a) 10 minutes
(b) 12 minutes ✓ UPSC's answer
(c) 15 minutes
(d) 25 minutes

Why the answer is (b)

• Pipe A fills 1/20 of the tank per minute, and Pipe B fills 1/30 of the tank per minute.

• When both pipes are opened simultaneously, their combined rate is the sum of their individual rates: 1/20 + 1/30.

• To add these fractions, find the least common multiple of 20 and 30, which is 60.

• Convert the rates: 1/20 = 3/60 and 1/30 = 2/60.

• The combined rate is 3/60 + 2/60 = 5/60 = 1/12 of the tank per minute.

• Therefore, the time taken to fill the tank completely is the reciprocal of the combined rate, which is 12 minutes.

Why the other options are wrong

(a) 10 minutes: 10 minutes is incorrect because the combined rate (1/12) is slower than Pipe A's individual rate (1/20), so the time must be greater than 20 minutes divided by 2, but specifically calculated as 12, not 10.
(c) 15 minutes: 15 minutes is incorrect because it does not correspond to the reciprocal of the sum of the individual rates (1/20 + 1/30 = 1/12).
(d) 25 minutes: 25 minutes is incorrect because opening both pipes simultaneously must result in a time less than the time taken by the slower pipe alone (30 minutes), and the calculation yields 12 minutes.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.