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Question

If $$12$$ men and $$16$$ boys can do a piece of work in $$5$$ days and $$13$$ men and $$24$$ boys can do it in $$4$$ days, how long will $$7$$ men and $$10$$ boys take to do it


Solution

$$ 5 (12 M + 16 B) =4 (13 M + 24 B )$$

$$ 60 M + 80 B = 52 M + 96 B $$

$$ 8M = 16 B $$

$$\therefore  M = 2B $$

Now , $$ 12 M + 16 B $$ Can do work in $$5$$ days 

So $$ 12 M + 8 M $$ can do work in $$5$$ days 

So $$20 M$$ can do work in $$5$$ days.

Now, $$7M + 10 B = 7M + 5 M = 12 M$$

Hence, if $$20 M$$ can do work in $$5$$ days 

$$ 12 M$$ can do work in $$ \dfrac{20\times 5}{12}$$

$$ = 8.33 \,\,days $$

Mathematics

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