If an amount of ₹ 1,50,000 is shared among A, B and C in the ratio of 2 : 3 : 5, then A receives the same amount as he would receive if another sum of money is shared between A, B and C in the ratio of 5 : 3 : 2. The ratio of ₹ 1,50,000 to the second amount of money is

### Concept & Ratio Equivalence Equate the specific amounts derived from two different total sums partitioned by their respective ratio distributions to find the relationship between the two totals. ### Step-by-Step Solution * Let the first amount be $T_1 = \text{₹ } 1,50,000$. * It is shared among $A$, $B$, and $C$ in the ratio $2 : 3 : 5$. (Total parts = 10) * $A$'s share from the first amount = $\frac{2}{10} \times 150000 = 2 \times 15000 = \text{₹ } 30,000$. * Let the second amount of money be $T_2$. * It is shared in the ratio $5 : 3 : 2$. (Total parts = 10) * $A$'s share from the second amount = $\frac{5}{10} \times T_2 = \frac{1}{2} T_2$. * The problem states $A$ receives the same amount in both cases: $$30000 = \frac{1}{2} T_2$$ * $T_2 = 30000 \times 2 = 60000$. * We need the ratio of the first amount to the second amount ($T_1 : T_2$). * Ratio = $150000 : 60000$. * Dividing both by 30000: $5 : 2$. ### Exam Strategy & Shortcut $A$'s share is $\frac{2}{10}$ of Amount 1 and $\frac{5}{10}$ of Amount 2. Since these shares are equal, $\frac{2}{10} \times A_1 = \frac{5}{10} \times A_2$. This simplifies directly to $2 A_1 = 5 A_2$, which means the ratio $\frac{A_1}{A_2} = \frac{5}{2}$. You don't even need to use the actual value of ₹ 1,50,000! ### Common Pitfall Unnecessarily calculating the shares of $B$ and $C$, which consumes time, or setting up the final ratio in the reverse order ($T_2 : T_1$ which is $2 : 5$). ### Final Answer Therefore, the correct answer is **5 : 2**.