Question
Two pipes can fill a tank in 40 and 48 minutes respectively and a waste pipe can empty 3 gallons per minutes. All the three pipes working together can fill the tank in 30 minutes, The capacity of the tank is-
Answer: Option D
Work done by the waste pipe in 1 minute
$$\eqalign{
& {\text{ = }}\frac{1}{{30}} - \left( {\frac{1}{{40}} + \frac{1}{{48}}} \right) \cr
& = \left( {\frac{1}{{30}} - \frac{{11}}{{220}}} \right) \cr
& = - \frac{1}{{80}}\left[ { - \,{\text{Nagetive sign means emptying}}} \right] \cr
& \therefore {\text{Volume of }}\frac{1}{{80}}{\text{ part = 3 galons}} \cr
& {\text{Volume of whole tank}} \cr
& {\text{ = }}\left( {3 \times 80} \right){\text{gallons}} \cr
& {\text{ = 240 gallons}}{\text{}} \cr} $$
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Work done by the waste pipe in 1 minute
$$\eqalign{
& {\text{ = }}\frac{1}{{30}} - \left( {\frac{1}{{40}} + \frac{1}{{48}}} \right) \cr
& = \left( {\frac{1}{{30}} - \frac{{11}}{{220}}} \right) \cr
& = - \frac{1}{{80}}\left[ { - \,{\text{Nagetive sign means emptying}}} \right] \cr
& \therefore {\text{Volume of }}\frac{1}{{80}}{\text{ part = 3 galons}} \cr
& {\text{Volume of whole tank}} \cr
& {\text{ = }}\left( {3 \times 80} \right){\text{gallons}} \cr
& {\text{ = 240 gallons}}{\text{}} \cr} $$
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