A water tank has a capacity of 25.25 kilolitres in an hour. An inlet pipe allows 5 kilolitres and 25 litres in a hour. An outlet pipe will empty the tank at the rate of 2.5 kilolitres in an hour. If the tank is empty and accidentally both the pipes are simultaneously opened, will the tank filled ? If it fills, how much of water will be filled in one hour ? How long will it take to fill the tank completely ?

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Solution

Dear Student,

(1) A tank can be filled by pipe A in 6 hours and pipe B in 8 hours. Both the pipes are opened and after 2 hours, pipe A is closed. In how many hours will pipe B fill the remaining tank ?

Part filled by pipe A in 1 hour = 1/6
Part filled by pipe B in 1 hour = 1/8
Part filled by pipe A and pipe B in 1 hour = $\frac{1}{6} + \frac{1}{8} = \frac{4 + 3}{24} = \frac{7}{24}$
Both pipes were opened for 2 hours.
So, Part filled by pipe A and pipe B in 2 hours = $2 \times \frac{7}{24} = \frac{7}{12}$
Remaining part to be filled = 1- $\frac{7}{12} = \frac{5}{12}$

This part should be filled by part B alone,

The time taken for this = $\frac{\frac{5}{12}}{\frac{1}{8}} = \frac{5}{12} \times \frac{8}{1} = \frac{10}{3} h o u r s$

$(2) . Time taken by pipe A to fill the tank alone = 12 hrs A' s 1 hour work = \frac{1}{12} Time taken by pipe B to fill the tank alone = 16 hrs B' s 1 hour work = \frac{1}{16} Time taken by pipe C to empty the tank = 8 hours So, C' s 1 hour work = \frac{1}{8} Now, (A + B + C)' S 1 hour work = \frac{1}{12} + \frac{1}{16} - \frac{1}{8} = \frac{4 + 3 - 6}{48} = \frac{1}{48} Hence, required time = 48 hours$

Regards

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