Question

If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, how long will 7 men and 10 boys take to do it?

Answer 1

12 men + 16 boys can do a piece of work in = 5 days
60 men + 80 boys can do a piece of work in = 1 day (i)
and 13 men + 24 boys can do the same work in = 4 days
52 men + 96 boys can do the same work in = 1 day (ii)
From (i) and (ii)
$\therefore$ 60 men + 80 boys = 52 men + 96 boys
$\Rightarrow$ 60 men - 52 men
= 96 boys - 80 boys
$\Rightarrow$ 8 men
= 16 boys
1 men $=\frac{16}{8}$
= 2 boys
Now, in first case,
12 men + 16 boys $=12\times 2+16$
$=24+16$
$=40boys$
In the second case,
7 men + 10 boys $=7\times 2+10$
= 14 + 10
= 24 boys
Now 40 boys can do a piece of work in = 5 days
1 boy can do the same work in $=5\times 40$ days
and 24 boys will do the same work in
$=\frac{5\times 40}{24}$ days
$=\frac{25}{3}$
$=8\frac{1}{3}$ days