Question

12 men or 8 boys can complete a work in 18 days. The time taken by 2 men and 4 boys to complete the same work with
taken by 3 men and 6 boys to complete the same work?​

Answer 1

Suppose that one man alone can finish the work in x days and one boy alone can finish it in y days. Then,

One man's one day's work =x1

One boy's one day's work =y1

∴ Eight men's one day's work =x8

12 boy's one day's work =y12

Since 8 men and 12 boys can finish the work in 10 days

10(x8+y12)=1⇒x80+y120=1  ..(i)

Again, 6 men and 8 boys can finish the work in 14 days.

∴14(x6+y8)=1⇒x84+y112=1 (ii)