A man, a woman and a boy can do a piece of work in 3 days, 4 days and 12 days respectively. How many boys should help a man and a woman to do the same piece of work in $1 \over 4$ day?



[ A ]    41
right
[ B ]    48
[ C ]    52
[ D ]    61
Answer : Option A
Explanation :
1 man does the work in $1 \over 4$ day $1\over 3$ x $1 \over 4$ = $1 \over 12$ part

1 woman does the work in $1 \over 4$ day $1 \over 4$ x $1 \over 4$ = $1 \over 16$ part

Total work done by one man and one woman = $1 \over 12$ + $1 \over 16$ = $4 + 3 \over 46$ = $7 \over 48$

So, Remaining work = 1 - $7 \over 48$ = $41 \over 48$ part

So, The number of boys = $41 \over 48$ $\times$ 48 = 41 boys

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