Question
Two pipe can fill a cistern in 3 hours and 4 hours respectively and a waste pipe can empty it in 2 hours. If all the three pipes are kept open, then the cistern will be filled in-
Answer: Option D
Part of the cistern filled in 1 hour
$$ = \frac{1}{3} + \frac{1}{4} - \frac{1}{2}$$
(Cistern filled by 1st pipe + Cistern filled by 2nd pipe – Cistern emptied by 3rd pipe )
$$\eqalign{
& \frac{{4 + 3 - 6}}{{12}} \cr
& = \frac{1}{{12}} \cr} $$
Hence, the cistern will be filled in 12 hours.
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Part of the cistern filled in 1 hour
$$ = \frac{1}{3} + \frac{1}{4} - \frac{1}{2}$$
(Cistern filled by 1st pipe + Cistern filled by 2nd pipe – Cistern emptied by 3rd pipe )
$$\eqalign{
& \frac{{4 + 3 - 6}}{{12}} \cr
& = \frac{1}{{12}} \cr} $$
Hence, the cistern will be filled in 12 hours.
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