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A pipe P can fill a tank in 12 min and another pipe R can fill it in 15 min. But, the 3rd pipe M can empty it in 6 min. The 1st two pipes P and R are kept open for double the 2.5 min in beginning and then the 3rd pipe is also opened. In what time is the tank emptied?
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- 30 min
- 25 min
- 45 min
- 35 min
Correct Option: C
According to the question,
Double the 2.5 min = 5 min
Now, part filled in 5 min = 5 x ( 1/12 + 1/15 ) = [5 x ( 5 + 4)]/60 = (5 x 9)/60 = 3/4
Part emptied in 1 min when P, R and M, all are opened. = 1/6 - ( 1/12 + 1/5 ) = 1/6 - (5 + 4)/60 = 1/60
One - sixtieth part is emptied in 1 min.
∴ Three - fourth part will be emptied in 60 x (3/4) = 15 x 3 = 45 min.