2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 men and 1 boy do the work?

• 2 men and 3 boys can do a piece of work in 10 days.
Thus, 20 men and 30 boys can do a piece of work in 1 day......(i)

• 3 men and 2 boys can do the same work in 8 days.
Thus, 24 men and 16 boys can do the same work in 1 day....(ii)

• Equating (i) and (ii) we get -
o 20 men + 30 boys = 24 men + 16 boys
o 4 men = 14 boys
o 2 men = 7 boys

• Substituting this in equation (i) we get

10 boys can do a piece of work in 10 days.
But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.

8 boys can do the same work in (10 × 10/8) = 12.5 days.