Question
Two taps A and B can fill a cistern in 12 min and 16 min
respectively. If both taps are opened together and at the end of 4 min, B tap is turned off, then how much time will it take to fill the cistern?Solution
Tap A fills the tank in 12 minutes → So, in 1 minute, it fills 1/12
Tap B fills the tank in 16 minutes → So, in 1 minute, it fills 1/16
Both taps are open for 4 minutes:
In 1 minute, together they fill: 1/12 + 1/16 = 7/48 ​
In 4 minutes, they fill: 7/48 × 4 = 28/48 =7/12 ​
B is turned off. Only A fills the rest.
Remaining to fill: 1−7/12 = 5/12
A fills 1/12 per minute, so time to fill 5/12: 5/12 ÷ 1/12 = 5 minutes
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