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?

#### Solution

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)

60 men + 80 boys = 52 men + 96 boys

⇒ 60 men – 52 men = 96 boys – 80 boys

⇒ 8 men = 16 boys

1 man =`16/8` = boys

**Now, in first case,**

12 men + 16 boys = 12 x 2 + 16 = 24+16 = 40 boys

**In the second case,**

7 men + 10 boys = 7 x 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 x 40 days

and 24 boys will do the same work in

`=(5xx40)/24` days

`=25/3`

`=8 1/3` days