Discussion

Explanation:

Let the amount of work to be done = LCM (12, 48, 32) = 96 units.

∴ Efficiency of a man = 96/48 = 2 units/day
Efficiency of a woman = 96/32 = 3 units/day
Let the efficiency of a boy = 'b' units/day

A man, a woman, and a child can do a piece of work in 12 days.

⇒ 96 = (2 + 3 + b) × 12
⇒ 8 = 2 + 3 + b
⇒ b = 3

∴ Efficiency of a boy = 3 units/day

⇒ Time taken by a boy to complete the work alone = 96/3 = 32 days.

Alternately,
Say the child takes C days to complete the work.

Amount of work all together can do in one day = $\frac{1}{12}$ of total work.

Amount of work Man can do in one day = $\frac{1}{48}$ of total work

Amount of work Woman can do in one day = $\frac{1}{32}$ of total work

Amount of work Child can do in one day = $\frac{1}{C}$ of total work.

According to question:

⇒ $\frac{1}{48}$ + $\frac{1}{32}$ + $\frac{1}{C}$ = $\frac{1}{12}$

⇒ $\frac{1}{C}$ = $\frac{1}{12}$- $\frac{1}{48}$ - $\frac{1}{32}$ = $\frac{1}{32}$

⇒ C = 32 days.

Hence, option (c).

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