Anand and Deepak started a business investing ₹ 22500 and ₹ 35000 respectively. Out of a total profit of ₹ 13800, Deepak's share is

### Concept & Profit Distribution Profits are distributed in proportion to the capital invested when the duration of investment is identical. $$ \text{Share of A} = \text{Total Profit} \times \left( \frac{\text{Ratio of A}}{\text{Total Ratio Parts}} \right) $$ ### Step-by-Step Solution * **Given:** * Anand's investment = ₹ $22500$ * Deepak's investment = ₹ $35000$ * Total profit = ₹ $13800$ * **Calculation/Deduction:** 1. Determine the profit-sharing ratio based on investments: $$\text{Anand} : \text{Deepak} = 22500 : 35000$$ 2. Simplify the ratio by removing two zeros: $$\text{Ratio} = 225 : 350$$ 3. Divide both numbers by their highest common factor ($25$): $$\text{Ratio} = 9 : 14$$ 4. Calculate the total number of ratio parts: $$\text{Total Parts} = 9 + 14 = 23$$ 5. Calculate Deepak's share of the total profit: $$\text{Deepak's Share} = 13800 \times \left(\frac{14}{23}\right)$$ $$\text{Deepak's Share} = 600 \times 14 = 8400$$ ### Exam Strategy & Shortcut Quickly simplify the ratio $22500 : 35000 \rightarrow 225 : 350 \rightarrow 9 : 14$. Knowing the total parts equal $23$, you can check if $138$ is divisible by $23$ ($23 \times 6 = 138$). The multiplier is $600$. Multiply Deepak's ratio part ($14$) by $600$ to get $8400$. ### Common Pitfall A common error is calculating Anand's share instead of Deepak's due to misreading the final question line. Always double-check whose share is requested before finalizing the calculation. ### Final Answer Therefore, the correct answer is **₹ 8400**.