6 men and 8 boys can do a piece of work in 7 days while 8 men and 12 boys do the same work in 5 days. How long would it take one boy to finish the same work?
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Solution :
Suppose 1 man alone can finish the work in x days and 1 boy alone can finish it in y days. <br> Then , 1 man's 1 day's work =
. <br> And, 1 boy's 1 day's work =
<br> 8 men and 12 boys can finish the work in 5 days <br>
( 8 men's 1 day's work ) + ( 12 boy's 1 day's work ) =
<br>
<br>
... (i), where
<br> Again, 6 men and 8 boys can finish the work in 7 days <br>
( 6 men's 1 day's work) + ( 8 boy's 1 day's work)
<br>
<br>
... (ii) <br> On multiplying (i) by 3, (ii) by 4 and subtracting the results, we get <br>
<br> On putting
in (ii), we get <br>
<br>
<br>
one man along can finish the work in 70 days, <br> and one boy alone can finish the work in 140 days.
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