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Time & Work

A man, a woman or a boy can do a piece of work in 3, 4 and 12 days respectively. How many boys must assist one man and one woman to do the work in one days ?

Option:
A. 5
B. 6
C. 8
D. 12
Answer: A . 5

Justification:

One man's 1 day's work = $1/3$
One woman's 1 day's work = $1/4$
One boy's 1 day's work = $1/12$
(1 man + 1 woman) 1 day's work
= ${1/3}+{1/4}={7/12}$
Remaining work = $1$ - ${7/12} = {5/12}$
Now, $1/12$ work in done by = $1$ boy $5/12$ work is done by
= ${1 * 5/12}/{1/12}$
= $12/1$ x $5/12 = 5$
Hence, 5 boys shpuld assist one man and one woman to finish the work. 

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