Quantitative Aptitude Ques 2346

Question: A cistern has three pipes A, B and C. A and B can fill it in 3 and 4 h, respectively and C can empty it in 1 h. If the pipes are opened at 3 pm, 4 pm and 5 pm, respectively on the same day, then cistern will be empty at

Options:

A) 7: 12 pm

B) 7: 15 pm

C) 7: 10 pm

D) 7: 18 pm

Show Answer

Answer:

Correct Answer: A

Solution:

  • 1 h work of pipe $ A=\frac{1}{3} $ 1 h work of pipe $ B=\frac{1}{4} $ 1 h work of pipe $ C=-\frac{1}{1} $ Total part fill by A and B in $ 2h=\frac{2}{3}+\frac{1}{4}=\frac{11}{12} $ and 1 h work of A, B and C $ =\frac{1}{3}+\frac{1}{4}-1=-\frac{5}{12} $ i.e. $ \frac{5}{12} $ part of tank can he emptied in 1 h.

$ \therefore $ Time taken to empty $ \frac{11}{12}part=\frac{11}{12}\times \frac{12}{5}=\frac{11}{5}h $ = 2 h 12 min

$ \therefore $ Required time $ \text{=}5,\text{pm+2},h,\text{12 min} $ = 7: 12 pm

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