A starts business with ₹ 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

### Concept & Formula Profit sharing ratio is based on equivalent investment, which is the product of Capital and Time. $$\frac{Profit_A}{Profit_B} = \frac{Capital_A \times Time_A}{Capital_B \times Time_B}$$ ### Step-by-Step Solution 1. A invested ₹ 3500 for the entire year, so A's time = 12 months. 2. B joined after 5 months, so B was invested for $12 - 5 = 7$ months. 3. Let B's capital contribution be $x$. 4. The ratio of their profits is given as 2 : 3. 5. Set up the equation: $\frac{3500 \times 12}{x \times 7} = \frac{2}{3}$ 6. Simplify the left side: $\frac{500 \times 12}{x} = \frac{2}{3}$ (by dividing 3500 by 7) 7. $\frac{6000}{x} = \frac{2}{3}$ 8. Cross-multiply: $18000 = 2x$ 9. $x = \frac{18000}{2} = 9000$. ### Exam Strategy & Shortcut A's equivalent capital = $3500 \times 12 = 42000$. This represents 2 units of profit. So, 1 unit of profit = $21000$. B needs 3 units of profit, so B's equivalent capital must be $3 \times 21000 = 63000$. Since B invests for 7 months, Capital = $\frac{63000}{7} = 9000$. ### Common Pitfall Using 5 months as B's time period instead of $12 - 5 = 7$ months. B joined *after* 5 months, meaning B's money was active for the remaining 7 months. ### Final Answer Therefore, the correct answer is **₹ 9000**.