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 the tank in 20 minutes, so in one minute it fills 1/20 of the tank.
• Pipe B fills the tank in 30 minutes, so in one minute it fills 1/30 of the tank.
• When both pipes are opened simultaneously, the combined rate per minute is 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the tank.
• Since together they fill 1/12 of the tank each minute, the time to fill the entire tank is 1 ÷ (1/12) = 12 minutes.
• Therefore, both pipes working together will fill the tank completely in 12 minutes, which corresponds to option (b).
Why the other options are wrong
- (a) 10 minutes
- 10 minutes would result from incorrectly assuming that two pipes together work twice as fast as the faster pipe alone (20 ÷ 2 = 10), ignoring that pipe B contributes less than pipe A.
- (c) 15 minutes
- 15 minutes would arise from the erroneous computation 1/20 + 1/30 = 1/15, which is arithmetically wrong; the correct sum is 5/60 = 1/12, not 1/15.
- (d) 25 minutes
- 25 minutes is simply the arithmetic mean of 20 and 30, i.e. (20 + 30)/2, which has no basis in the rate-of-work formula; combined rates are added as reciprocals, not averaged as times.
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.