Quantitative Aptitude Ques 815
Question: A and B together can do a work in 12 days. B and C together do it in 15 days. If As efficiency is twice that of C, then the number of days required for B alone to finish the work, is
Options:
A) 60
B) 20
C) 30
D) 15
Show Answer
Answer:
Correct Answer: B
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} $ and $ \frac{1}{2x}+\frac{1}{y}=\frac{1}{15} $
$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{15}-\frac{1}{2x} $ Solving, $ \frac{1}{12}-\frac{1}{x}=\frac{1}{15}-\frac{1}{2x} $
$ \Rightarrow $ $ \frac{1}{x}-\frac{1}{2x}=\frac{1}{12}-\frac{1}{15} $
$ \Rightarrow $ $ \frac{1}{2x}=\frac{5-4}{60} $
$ \Rightarrow $ $ x=30 $
$ \Rightarrow $ $ \frac{1}{y}=\frac{1}{12}-\frac{1}{x}=\frac{1}{12}-\frac{1}{30} $ $ =\frac{5-2}{60}=\frac{3}{60}=\frac{1}{20} $
$ \therefore $ $ y=20 $
BETA
