Question

2 men and 5 boys together can finish a pice of work in 4 days while 3 men and 6 boys can finish it in 3 days ..
find the time taken by one man to finish the work

Answer 1

let one man can do whole work in x days and a boy be y

then,1 man's work =1/x

and,1 boy's work=1/y

A/q

2/x+5/y=1/4

2a+5b=1/4 ....(1) where 1/x=a,1/y=b

also

3/x+6/y=1/3

3a+6b=1/3....(2)

multilply (1)by 3 and (2) by 2

6a+15b=3/4

6a+12b=2/3

subtract

3b=1/12

b=1/36

put b=1/36 in (1)

2a+5*1/36=1/4

2a=1/4-5/36

2a=1/9

a=1/18

b=1/x=1/36

x=36

a=1/y=1/18

y=18