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If 9 men and 12 boys can do a piece of w...

If 9 men and 12 boys can do a piece of work in 4 days and 4 men and 16 boys can do the
same work in 6 days, how long will 6 men and 24 boys take to complete the same work?

Text Solution

Verified by Experts

Given that,9m+12b can do the work in 4days and 4m+16b can do the same work in 6 days.
`:. 4(9m+12b)=6(4m+16b) implies m=4b`
Now, 9m+12b=9(4b)+12b=48b and
`6m+24b=6(4b)+24b=48b`
`:.` 6 men and 24 boys also take 4 days to complete the work.
ALTERMATE METHOD
(4m+16b) can do the work in 6 days.
`implies (3)/(2)(4m+16b)` can do the work in `(6xx(2)/(3))` days.
`implies (6m+24b)` can do the work in 4 days.
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