Question

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and one boy alone to finish the work.​

Answer 1

Step-by-step explanation:

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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