Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.
Correct Answer: Description for Correct answer:
Part filled by 1st pipe = \( \Large \frac{1}{20} \)
Part filled by 2nd pipe in 1 min = \( \Large \frac{1}{24} \)
Part filled by all the pipes in 1 min = \( \Large \frac{1}{15} \)
Work done by the waste pipe in 1 min
= \( \Large \frac{1}{15}- \left(\frac{1}{20}+\frac{1}{24}\right)=\frac{1}{15}- \left(\frac{6+5}{120}\right) \)
= \( \Large \frac{1}{15}-\frac{11}{20} \)
= \( \Large \frac{8-11}{120}= \left(-\frac{3}{120}\right)= \left(-\frac{1}{40}\right) \) [-ve sign indicates emptying]
Now, volume of \( \frac{1}{40} \) part = 6 gallon
Therefore, Volume of whole tank = \( \Large 40 \times 6 \) = 240 gallon
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