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.