A sum of ₹ 6100 was divided among 8 men, 10 women and 12 children in such a way that each man received 25\% more than a woman and each woman received $25 \%$ more than a child. How much did each woman receive?
(a)₹ 201.68
(b)₹ 203.68
(c)₹ 206.08
(d)₹ 206.68
Answer
Answer (as printed): C
Explanation
Let the amount received by each child be ₹ $x$. Then, amount received by each woman $=125 \%$ of $₹ x$ $$=₹ \frac{5 x}{4} .$$ Amount received by each man $=125 \%$ of $₹ \frac{5 x}{4}=₹ \frac{25 x}{16}$. $$\begin{aligned} & \therefore 8 \times \frac{25 x}{16}+10 \times \frac{5 x}{4}+12 x \\ & =6100 \Rightarrow \frac{25 x}{2}+\frac{25 x}{2}+12 x=6100 \Rightarrow 74 x=6100 \times 2 \\ & \Rightarrow x=\left(\frac{6100 \times 2}{74}\right) . \end{aligned}$$ Hence, amount received by each woman $$=₹\left(\frac{5}{4} \times \frac{6100 \times 2}{74}\right)=₹ \frac{7625}{37}=₹ 206.08 .$$
Explanation as extracted from the printed page; notation may be imperfect.