Question: A man and. a boy working together can complete a work in 24 days. If for the last 6 days, the man alone does the work, then it is completed in 26 days. How long will the boy take to complete the work alone?
Options:
A) 72 days
B) 73 days
C) 49 days
D) 62 days
Show Answer
Answer:
Correct Answer: A
Solution:
- Let man’s 1 day’s work $ =\frac{1}{m} $
and boy’s 1 day’s work $ =\frac{1}{n} $
1 day’s work of man and boy $ =\frac{1}{24} $
Man’s 6 days’ work $ =\frac{6}{m} $
Now, for 20 days, both man and boy do the work and for last 6 days, only man does the work.
According to the question,
$ \frac{1}{m}+\frac{1}{n}=\frac{1}{24} $
(i)
$ \Rightarrow $ $ 20( \frac{1}{m}+\frac{1}{n} )+\frac{6}{m}=1 $
$ \Rightarrow $ $ ( 20\times \frac{1}{24} )+\frac{6}{m}=1 $ [from Eq. (i)]
$ \Rightarrow $ $ \frac{6}{m}=( 1-\frac{20}{24} )=\frac{4}{24}=\frac{1}{6} $
$ \Rightarrow $ $ \frac{1}{m}=\frac{1}{36} $
Now from Eq. (i) $ \frac{1}{m}+\frac{1}{n}=\frac{1}{24} $
$ \Rightarrow $ $ \frac{1}{36}+\frac{1}{n}=\frac{1}{24} $
$ \Rightarrow $ $ \frac{1}{n}=( \frac{1}{24}-\frac{1}{36} )=\frac{1}{72} $
Hence, the boy alone can do the work in 72 days.
BETA
