Question

one man and 2 boys can do a pice of work in 12 days .which could be done in 6 days by 3 men and one boy. how long would it take one man to do it

Answer 1

let 1 man needs x days to complete the work

let 1 boy needs y days to complete the work

so one mans one day work =1/x

and one boys one day work =1/y


now,

1/x + 2/y = 1/12

2x + y / xy = 1 /12

24x + 12y = xy ------( 1 )

also ,

3/x + 1/y = 1/6

x + 3y / xy = 1/6

6x + 18 y = xy ------ ( 2 )

from 1 and 2

24x + 12y = 6x + 18 y

18 x = 6y

x / y = 6/18 = 1 /3

y = 3x

putting this value in eq 1 we get

24x + 12y = xy ------( 1 )

24x + 12*3x = x *3x

24x + 36x = 3x^2

60x = 3x^2

x = 20

so one man needs 20 days to complete the work