Question

One man can do as much work in one day as a woman can do in 2 days. A child does one-third the work in a day as a woman. If an estate-owner hires 39 pairs of hands — men, women, and children — in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the day's work, what must the daily wages of a child be, if the wages are proportional to the amount of work done?

• A. Rs. 14
• B. Rs. 5
• C. Rs. 20
• D. Rs. 7

Hint:

In wage distribution problems, always link wages to actual work output, compute per unit pay, then apply to each worker individually.

Answer 1

The Correct Option is A

First, let's determine the work rates:
- Let the work done by a man in 1 day = $1$ unit (baseline).
- A woman takes 2 days to do the same work, so in 1 day, a woman does $1/2$ unit.
- A child does one-third the work of a woman, so in 1 day, a child does $(1/3) \times (1/2) = 1/6$ unit.
Now, they are hired in the ratio: Men : Women : Children = $6 : 5 : 2$.
Total number of workers = $6 + 5 + 2 = 13$ parts.
Since there are 39 workers in total, each part corresponds to $39 / 13 = 3$ workers.
Thus:
Number of men = $6 \times 3 = 18$.
Number of women = $5 \times 3 = 15$.
Number of children = $2 \times 3 = 6$.
Total work done in 1 day =
From men: $18 \times 1 = 18$ units.
From women: $15 \times \frac{1}{2} = 7.5$ units.
From children: $6 \times \frac{1}{6} = 1$ unit.
Total = $18 + 7.5 + 1 = 26.5$ units.
Wages are proportional to work done, so total wages Rs. 1113 corresponds to 26.5 units of work.
Rate per unit work = $1113 / 26.5 = 42$ Rs per unit.
Work done by one child in a day = $1/6$ unit.
Wage for one child = $42 \times \frac{1}{6} = 7$ Rs. Wait — this is not matching option (A), so let's check logic.
Actually, 1 child's total daily wage = Work rate of child $\times$ Rs per unit work. But we must recall there are multiple children and wages are per individual. The calculation $42 \times \frac{1}{6}$ is indeed per child: = Rs. 7. This matches option (D), not (A).
Hence, the correct answer should be $\boxed{\text{Rs. 7}}$.