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A cistern has 3 pipes A, B and C, A and B can fill it in 2 and 3 hours respectively. C is a waste pipe. If all the 3 pipes be opened at once, 7/24 of the cistern will be filled up in 30 minutes. In what time can C empty the full cistern ?
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- 3 hours
- 4 hours
- 5 hours
- 6 hours
Correct Option: B
∵ 7/24 of the cistern will be filled up in 1/2 hr.
∴ The whole of the cistern will be filled up in (1/2) x (24/7) = 12/7 hrs.
Let the pipe C be empty the whole cistern in h hours
Now, applying the given rule we have,
(2 x 3 x h) / (3 x h + 2 x h - 2 x 3) = 12/7
or 42h = 60h - 72
∴ h = 4 hours.
