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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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- 38 min
- 22 min
- 42 min
- 45 min
Correct Option: D
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.
