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One pipe can fill the tank in 21 minutes while another pipe can empty completely filled tank in 24 minutes. If both the pipes are operated togeth
Question

One pipe can fill the tank in 21 minutes while another pipe can empty completely filled tank in 24 minutes. If both the pipes are operated together on empty tank, how long (in minutes) will it take to fill one-fourth of the tank?​

A.

42

B.

126

C.

84

D.

168

Correct option is A

Given:

Fill pipe rate = fills tank in 21 min 

121\frac{1}{21}​ tank/min

Empty pipe rate = empties tank in 24 min 

124-\frac{1}{24}​ tank/min

Both start on an empty tank; find time to fill  14\frac14​ tank.

Formula Used:

Time =WorkRate. \dfrac{\text{Work}}{\text{Rate}}.​​

Solution:
Net rate =121124=87168=1168= \frac{1}{21} - \frac{1}{24} = \frac{8-7}{168} = \frac{1}{168}​ tank/min.

Time to fill 14\frac14 tank =141168=1684=42 \dfrac{\frac14}{\frac{1}{168}} = \dfrac{168}{4} = 42​ minutes.

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