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.
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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
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