A, B and C enter into a partnership by making investments in the ratio 3 : 5 : 7. After a year, C invests another ₹ 337600 while A withdraws ₹ 45600. The ratio of investments then changes to 24 : 59 : 167. How much did A invest initially?

### Concept & Equating Ratios When an initial ratio is given, assign variables ($3x, 5x, 7x$). Apply the stated absolute changes (additions/withdrawals) to form expressions for the new amounts. Equate the ratio of these new expressions to the given final ratio to solve for the variable. ### Step-by-Step Solution * Let the initial investments of A, B, and C be $3x, 5x, \text{ and } 7x$ respectively. * **Changes after one year:** * A's new investment = $3x - 45600$ * B's new investment = $5x$ (no change mentioned) * C's new investment = $7x + 337600$ * **New Ratio:** * The new investments are in the ratio $24 : 59 : 167$. * $(3x - 45600) : 5x : (7x + 337600) = 24 : 59 : 167$ * **Solving for x:** * We can use any two parts of the ratio to form an equation. Using A and B is easiest because B's term is simple ($5x$). * $\frac{3x - 45600}{5x} = \frac{24}{59}$ * Cross-multiply: * $59(3x - 45600) = 24(5x)$ * $177x - 2690400 = 120x$ * $177x - 120x = 2690400$ * $57x = 2690400$ * $x = \frac{2690400}{57} = 47200$ * **Calculate A's Initial Investment:** * A's initial investment = $3x$ * $3 \times 47200 = 141600$ ### Exam Strategy & Shortcut Always choose the terms that create the simplest equation. Pairing A and B ($\frac{3x - \dots}{5x}$) avoids multiplying large numbers like $167$ or $337600$ until absolutely necessary. ### Common Pitfall Using the $C$ term to solve for $x$ makes the arithmetic much more prone to errors due to large multiplication steps. ### Final Answer Therefore, the correct answer is **₹ 141600**.