Question

8 men and 12 boys finish work in 10 days while 6 men and 8 boys can finish in 14 days. find the time taken by 1 man alone to finish the work​

Answer 1

let the no. of men and boy be x and y days

one men one day work = 1/x

one boy one day work =1/y

Therefore,

8 men one day work = 8/x

12 boys one day work =12/y

since 8 men and 12 boy can finish the work in 10 days

10(8/x+12/y)=1

80/x+120/y=1...........(1)

and 14(6/x+8/y)=1

84/x+112/y=1..............(2)

let 1/x=u and1/y=v

80u +120v-1=0

84u+112v-1=0

by cross multiplication ,we have,

u/-120+112 = -v/-80+84 = 1/ 80×112-120×84

implyed that ,

u/-8 = v/-4 = 1/-1120

imply that,

u = -8/-1120 = 1/140 and v = -4/-1120 = 1/280

now, u = 1/140

1/x=1/140

x =140 days

and,v = 1/280

1/y=1/280

y = 280 days

thus , one man complete the work in 140 days . one boy complete the work in 280 days