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
