two taps A and B can fill a tank in 12 hours and 15 hours respectively and outlet pipe C can empty a tank in 10 hours find the time taken to empty a tank if all the three pipes are opened together
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Two pipes, A and B, fill a tank in 15 hours and 20 hours respectively while a third pipe, C, can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In how much time will the tank be full?
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3 ANSWERS
Alpana Chakraborty, former Post Graduate Teacher. at Govt of Tripura (1978-2015)
Answered Jan 3
As given in the Q ,
Pipe A can fill the tank in 15 hours
So , in 1 hour A pipe can fill 1/15 th part of the tank .
Pipe B can fill the tank in 20 hours
So ,in 1 hour B pipe can fill 1/20 th pat of the tank .
In 1 hour A&B together can fill 1/15 +1/20 = 7/60 part of the tank . Now , C can empty the tank in 25 hours .
In 1 hour C pipe can empty 1/25 th part of the tank .
If all the three pipes are kept open ,in 1 hour ,60/7 — 1/25 = 23/300 part of the tank get filled. Acc. to the question ,all the three pipes kept open for 10 hours .
So ,in 10 hours 23/300 ×10 =23/30 part of the tank get filled . Now pipe c is closed after 10 hours .
So the reaining 1–23/30 = 7/30 part of the tank can be filled by A&B pipe in 7/30 ÷7/60 = 7/30 ×60/7 = 2 hours
Ans: 2 hours .