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, woman 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 be the daily wages of a child if the wages are proportional to the amount of work done?

Using the given ratios, let the efficiency of a child be 1 unit per day, meaning a woman is 3 units and a man is 6 units. Out of 39 total workers, the ratio 6:5:2 means there are 18 men, 15 women, and 6 children. Their total work units are 108 plus 45 plus 6, which equals 159 units. The total wage of Rs. 1113 divided by 159 units gives Rs. 7 per unit, so a child receives Rs. 7.

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