question_answer

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?

A) 4

B) 8

C) 6

D) Cannot be determined

E) None of the above

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.