Dilip, Ram and Avtar started a shop by investing ₹ 2700, ₹ 8100 and ₹ 7200 respectively. At the end of one year, the profit earned was distributed. If Ram's share was ₹ 3600, what was their total profit?

### Concept & Reverse Profit Calculation When you are given one partner's profit share and the investment ratio, you can find the value of a single "ratio part" and use it to determine the total profit. $$ \text{Total Profit} = \text{Value of One Part} \times \text{Total Parts} $$ ### Step-by-Step Solution * **Given:** * Investments: Dilip = ₹ $2700$, Ram = ₹ $8100$, Avtar = ₹ $7200$. * Time period is identical for all (1 year). * Ram's profit share = ₹ $3600$. * **Calculation/Deduction:** 1. Find the profit-sharing ratio (which equals the investment ratio): $$\text{Dilip} : \text{Ram} : \text{Avtar} = 2700 : 8100 : 7200$$ 2. Simplify by dividing by $100$: $$\text{Ratio} = 27 : 81 : 72$$ 3. Divide by their highest common factor ($9$): $$\text{Ratio} = 3 : 9 : 8$$ 4. Calculate total parts in the ratio: $$\text{Total Parts} = 3 + 9 + 8 = 20$$ 5. Equate Ram's ratio parts to his actual profit share: $$9 \text{ parts} = 3600$$ $$1 \text{ part} = \frac{3600}{9} = 400$$ 6. Calculate total profit using the total parts: $$\text{Total Profit} = 20 \text{ parts} \times 400 = 8000$$ ### Exam Strategy & Shortcut Simplify the ratio quickly: $27:81:72 \implies 3:9:8$. You know Ram represents $9$ parts. Mentally map $9 \rightarrow 3600$, which means a multiplier of $400$. The total is $20$ parts. $20 \times 400 = 8000$. The whole calculation can be done mentally in under 15 seconds. ### Common Pitfall A mistake is trying to set up a complex algebraic equation (e.g., $3x + 9x + 8x = Y$) and getting lost in variables. The unitary method (finding the value of 1 part) is much faster and less prone to error. ### Final Answer Therefore, the correct answer is **₹ 8000**.