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Pipes A and B can fill an empty cistern in 52 minutes and 65 minutes, respectively. Both Pipe A and Pipe B are opened together. After how much ti
Question

Pipes A and B can fill an empty cistern in 52 minutes and 65 minutes, respectively. Both Pipe A and Pipe B are opened together. After how much time should Pipe A be turned off so that the empty cistern is completely filled in a total of 60 minutes?

A.

20 min

B.

5 min

C.

15 min

D.

4 min

Correct option is D

Given:

Pipe A fills the cistern in 52 minutes

Pipe B fills the cistern in 65 minutes

Both pipes are opened together

The cistern is completely filled in 60 minutes

Concept Used:
If a pipe fills 1 tank in t minutes, its rate is 1t\frac{1}{t}​ per minute.
Total work = 1 (full tank)

Solution:

Pipe A is turned off after x minutes

Work by A in x minutes = x52\frac{x}{52}

Work by B in 60 minutes = 6065\frac{60}{65}

x52+6065=1\frac{x}{52} + \frac{60}{65} = 1​​

x52=16065=565\frac{x}{52} = 1 - \frac{60}{65} = \frac{5}{65}​​

x =565×52=26065=4 \frac{5}{65} \times 52 = \frac{260}{65} = 4 min

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