A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open 5 min in the beginning and then the third pipe is also opened.Time taken to empty the cistern is?

Question

Accepted Answer

Let the number of minutes taken to empty the cistern be T min.
According to the questions,
T/6 - (T + 5)/12 - (T + 5)/15 = 0
⇒ T/6 - T/12 - 5/12 - T/12 - T/12 - T/15 = 0
⇒ T/6 - T/12 - T/15 = 5/12 + 5/15
⇒ (10T - 5T - 4T)/ 60 = (25 + 20)/60
⇒ T/60 = 45/60
⇒ T = 45 min.

A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open 5 min in the beginning and then the third pipe is also opened.Time taken to empty the cistern is?

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