2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?

Explanation

Let 1 man can do a piece of work in x days while a boy can do a piece of work in y ways.
`therefore` One man's one day work = `(1)/(x)`
and one boy's one day work = `(1)/(y)`
According to given conditions,
`(2)/(x) + (7)/(y) = (1)/(4) " ...(1)"`
and `(4)/(x) + (4)/(y) = (1)/(3) " ...(2)"`
Multiplying equation (1) by 2 and (2) by 1, we get
`(4)/(x) + (14)/(y) = (1)/(2)` ...(3)
`(4)/(x) + (4)/(y) = (1)/(3)` ...(4)
Subtracting equation (4) from (3), we get
`(14)/(y) - (4)/(y) = (1)/(2) - (1)/(3)`
`implies (10)/(y) = (1)/(6)`
implies y = 60
Substituting y = 60 in equation (1), we get
`(2)/(x) + (7)/(60) = (1)/(4) implies (2)/(x) = (1)/(4) - (7)/(60)`
implies `(2)/(x) = (8)/(60)`
implies 8x = 120 or x = 15
Hence, one man would do the work in 15 days and one boy in 60 days.