Question: 2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
Options:
A) 4
B) 8
C) 6
D) Cannot be determined
E) None of the above
Show Answer
Answer:
Correct Answer: B
Solution:
- 1 man’s one day work $ =\frac{1}{12} $
1 woman’s one day work $ =\frac{1}{18} $
1 child’s one day work $ =\frac{1}{24} $
1 man can finish the work in 12 days
1 woman can finish the work in 18 days
1 child can finish the work in 24 days
$ \Rightarrow $ 12 men $ \equiv $ 18 women $ \equiv $ 24 children
$ \Rightarrow $ 2 men $ \equiv $ 3 women $ \equiv $ 4 children
Now, 3 women + 4 children = 4 men
Part of work done by 4 men in 1 day $ =\frac{4}{12}=\frac{1}{3} $
Remaining work $ =1-\frac{1}{3}=\frac{2}{3} $
Remaining $ \frac{2}{3} $ work will be finished by 1 man in
$ \frac{2}{3}\times 12=8,days $
To finish the work In 1 day we require 8 more men.
BETA
