Question

8 men can dig pit in 20 days.if a man works half as much again as a boy,then 4 men and 9 boys can dig a similar pit in

Answer 1

1boy=2men
9boys=18men
hence answer is 80/11 hours

Answer 2

4 men and 9 boys can pit a dig in 16 days

Given:

Work of a man = Boy’s one day work +$\frac{1}{2}$ work of a boy

To find:

Number of days needed for 4 men and 9 boys to pit a dig.

Solution  

Work of a man = Boy’s one day work $+\frac{1}{2}$  work of a boy

Therefore, One day work of a man $=\frac{3}{2}$ boy’s one day work

1 man $=\frac{3}{2}$  boy

1 boy $= \frac{2}{3}$  man

9 boy = 6 man $\rightarrow(1)$

Hence form equation (1)

work done by 4 men + 9 boys = work done by 4 men + 6 men = work done by 10 men $\rightarrow(2)$

Now, Let 10 men can complete a work in n days.

Given that,  

20 men can dig a pit and completed the work in 8 days.

Therefore,

$\begin{array}{l}{10 \times n=20 \times 8} \\\\ {n=\frac{20 \times 8}{10}=16}\end{array}$