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

## Concept & Logic This problem is solved by establishing relative ratios between the shares of different individuals. By expressing the share of a man and a woman in terms of a boy's share, we convert a multi-variable problem into a single-variable linear equation. $$ Man = Woman + Boy $$ $$ Woman = 2 \times Boy $$ ## Step-by-Step Solution * **Given:** Total money = ₹ 370. Groups = 10 Men ($M$), 12 Women ($W$), 20 Boys ($B$). Relationship 1: $M = W + B$ Relationship 2: $W = 2B$ * **Deduction:** Substitute the value of $W$ into Relationship 1 to express $M$ entirely in terms of $B$: $M = 2B + B = 3B$. * **Calculation:** Set up the total sum equation: $10M + 12W + 20B = 370$ * **Substitution:** Replace $M$ and $W$ with their equivalent in $B$: $10(3B) + 12(2B) + 20B = 370$ $30B + 24B + 20B = 370$ $74B = 370$ * **Calculation:** Solve for $B$: $B = \frac{370}{74} = 5$. Each boy receives ₹ 5. * **Calculation:** The question asks for the amount received by 10 men. Each man receives $M = 3B = 3 \times 5 = 15$. 10 men receive $10 \times 15 = 150$. ## Exam Strategy & Shortcut Direct ratio mapping is the fastest approach. Let Boy = 1 unit. Woman = 2 units. Man = 1 + 2 = 3 units. Total equivalent units for the group = $10(3) + 12(2) + 20(1) = 30 + 24 + 20 = 74$ units. 74 units = ₹ 370 $\rightarrow$ 1 unit = ₹ 5. 10 men represent 30 units. $30 \times 5 = 150$. ## Common Pitfall Solving for the share of one man (₹ 15) and stopping there, forgetting that the question specifically asks for the combined amount received by **10 men**. Always re-read the final sentence before selecting an option. ## Final Answer Therefore, the correct answer is **₹ 150**.