SATHEE: Quantitative Aptitude Ques 476

Quantitative Aptitude Ques 476

Question: A and B together can do a work in 12 day, B and C together do it in 15 days. If A’s efficiency is twice that of C, then the day- required for C alone to finish the work is

Options:

A) 45 days

B) 50 days

C) 60 days

D) 70 days

Show Answer

Answer:

Correct Answer: C

Solution:

Let A can do the work in x days, then C can do the work in 2x days. Let B can do that work in y days.

$ \therefore $ $ \frac{1}{x}+\frac{1}{y}=\frac{1}{12} $

$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{12}-\frac{1}{x} $ (i) and $ \frac{1}{2x}+\frac{1}{y}=\frac{1}{15} $

$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{15}-\frac{1}{2x} $ (ii) From Eqs. (i) and (ii), we get $ \frac{1}{12}-\frac{1}{x}=\frac{1}{15}-\frac{1}{2x} $

$ \Rightarrow $ $ \frac{1}{2x}-\frac{1}{x}=\frac{1}{15}-\frac{1}{12} $

$ \Rightarrow $ $ \frac{1-2}{2x}=\frac{4-5}{60} $

$ \Rightarrow $ $ \frac{-1}{2x}=\frac{-1}{60} $
$ \Rightarrow $ $ x=30 $

$ \therefore $ C takes time $ =2\times 30=60,days $

Quantitative Aptitude Ques 475

Quantitative Aptitude Ques 477

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