Anil, Kamal and Vini Invested ₹ 8000, ₹ 4000 and ₹ 8000 respectively in a business. Anil left after six months. If after eight months, there was a gain of ₹ 4005, then what will be the share of Kamal?

### Concept & Profit Distribution over Custom Timeframe Profit shares are based on the product of investment and active time. Always check the total timeframe over which the profit is evaluated. If the gain is evaluated at 8 months, use 8 months as the maximum duration. $$Profit\ Ratio = (C_1 \times T_1) : (C_2 \times T_2) : (C_3 \times T_3)$$ ### Step-by-Step Solution 1. Identify the investment amount and time period for each person. The total timeframe is 8 months. 2. Anil: Invested ₹ 8000. Left after 6 months. Equivalent capital = $8000 \times 6 = 48000$. 3. Kamal: Invested ₹ 4000. Stayed for the entire 8 months. Equivalent capital = $4000 \times 8 = 32000$. 4. Vini: Invested ₹ 8000. Stayed for the entire 8 months. Equivalent capital = $8000 \times 8 = 64000$. 5. Find the profit sharing ratio (Anil : Kamal : Vini): $48000 : 32000 : 64000$ 6. Simplify the ratio by dividing by 16000: $3 : 2 : 4$. 7. The total number of ratio parts = $3 + 2 + 4 = 9$ parts. 8. The total gain (profit) is ₹ 4005. 9. Kamal's share is $\frac{2}{9}$ of the total profit. Kamal's share = $\frac{2}{9} \times 4005$ 10. Calculate: $4005 \div 9 = 445$. 11. Kamal's share = $2 \times 445 = 890$. ### Exam Strategy & Shortcut Cancel common zeroes immediately before multiplying. The capitals are in the ratio 2:1:2 (dividing 8000, 4000, 8000 by 4000). Time periods are 6, 8, and 8. Profit ratio = $(2 \times 6) : (1 \times 8) : (2 \times 8) = 12 : 8 : 16$. Simplify to $3 : 2 : 4$. Kamal's share = $\frac{2}{9} \times 4005 = 890$. ### Common Pitfall Assuming the business year is 12 months by default, even though the problem explicitly states the gain was evaluated "after eight months". Using 12 months for Kamal and Vini will lead to incorrect ratios. ### Final Answer Therefore, the correct answer is **₹ 890**.