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1. Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18 : 10 : 12 and if the wages of an individual man, woman and child is in ratio 6 : 5 : 3, then how much a woman earn in a day?

A. Rs. 120

B. Rs. 150

C. Rs. 250

D. Rs. 400

Solution:

Ratio of number of men, women and children,

\begin{aligned} = \frac{18}{6} : \frac{10}{5} : \frac{12}{3} \\ = 3 : 2 : 4 \end{aligned}

Total (Men + Women + Children) = 18
3X + 2X + 4X = 18
9X = 18
X = 2
Hence, number of women = 2X = 2 × 2 = 4
Share of all women =

\frac{10 \times 4000}{40}

= Rs. 1000 [18 + 10 + 12 = 40]
Thus, share of each woman =

\frac{1000}{4}

= Rs. 250

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