This is not reflective of an actual GMAT problem.jahid43 wrote:2 men and 3 boys can do a piece of work in 10 days which 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men 1 boy do the work?
That said, we can glean some take-aways from the solution, so here goes:
Let the job = 800 units.
Since 2 men and 3 boys take 10 days to produce 800 units, the rate for 2M + 3B = w/t = 800/10 = 80 units per day.
Thus:
2M + 3B = 80 units per day.
Since 3 men and 2 boys take 8 days to produce 800 units, the rate for 3M + 2B = w/t = 800/8 = 100 units per day.
Thus:
3M + 2B = 100 units per day.
Adding the two equations, we get:
(2M + 3B) + (3M + 2B) = 80 + 100
5M + 5B = 180
M + B = 36 units per day.
Subtracting the first equation from the second, we get:
(3M + 2B - (2M + 3B) = 100 - 80
M - B = 20 units per day.
Adding together M+B=36 and M-B=20, we get:
(M+B) + (M-B) = 36 + 20
2M = 56 units per day.
M = 28 units per day.
Since M=28 and M-B = 20, B = 8 units per day.
Thus:
Rate for 2M + B = 2*28 + 8 = 64 units per day.
Time for 2M + B to produce 800 units = w/r = 800/64 = 100/8 = 12.5 days.
