If ₹ 370 are divided among 10 men, 12 women and 20 boys such that each man gets an amount equal to that received by one woman and one boy together and each woman gets twice the amount received by a boy, then the amount received by 10 men would be
(a)₹ 100
(b)₹ 120
(c)₹ 130
(d)₹ 150
Answer
Answer (as printed): D
Explanation
Suppose each boy gets ₹ $x$. Then, each woman gets ₹ $2 x$ and each man gets ₹ $(x+2 x)$ i.e., ₹ $3 x$. So, $10 \times 3 x+12 \times 2 x+20 x=370 \Leftrightarrow 30 x+24 x+20 x$ $$\begin{aligned} & =370 \Leftrightarrow 74 x \\ & =370 \Leftrightarrow x=5 \end{aligned}$$ ∴ Amount received by 10 men $=30 x=₹(30 \times 5)$ $$\text { = ₹ } 150 .$$
Explanation as extracted from the printed page; notation may be imperfect.