Quantitative Aptitude Ques 1783
Question: Three pipes A, B and C can fill a tank separately in 8 h, 10 h and 20 h, respectively. Find the time taken by all the three pipes to fill tank when the pipes are opened together.
Options:
A) $ 5\frac{7}{11}h $
B) $ 4\frac{7}{11}h $
C) $ 8\frac{7}{11}h $
D) $ 3\frac{7}{11}h $
E) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
- Part filled by A in $ 1h=\frac{1}{8} $ Part filled by B in $ 1h=\frac{1}{10} $ Part filled by C in $ 1h=\frac{1}{20} $ Part filled by (A + B + C) in 1 h $ =\frac{1}{8}+\frac{1}{10}+\frac{1}{20}=\frac{5+4+2}{40}=\frac{11}{40}h $
$ \therefore $ Required time to fill the tank $ =\frac{40}{11}h=3\frac{7}{11}h $ Alternative method Here, $ m=8, $ $ n=10 $ and $ p=20 $
$ \therefore $ Required time to fill the tank $ =\frac{mp}{mn+np+mp} $ $ =\frac{8\times 10\times 20}{8\times 10+10\times 20+8\times 20} $ $ =\frac{1600}{80+200+160}=\frac{1600}{440} $ $ =\frac{40}{11}=3\frac{7}{11}h $
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