Simran started a software business by investing ₹ 50000. After six months, Nanda joined her with a capital of ₹ 80000. After 3 years, they earned a profit of ₹ 24500. What was Simran's share in the profit?

### Concept & Multi-Year Profit Distribution Calculate the profit-sharing ratio by multiplying each partner's capital by the number of months it was invested. When the result is not among the explicit numerical options, trust your calculation over guessing. $$ \text{Share of A} = \text{Total Profit} \times \left( \frac{\text{Ratio Part of A}}{\text{Total Ratio Parts}} \right) $$ ### Step-by-Step Solution * **Given:** * Total duration = $3$ years = $36$ months. * Simran's capital = ₹ $50000$ (active for $36$ months). * Nanda's capital = ₹ $80000$ (joined $6$ months later). * Total Profit = ₹ $24500$. * **Calculation/Deduction:** 1. Determine Nanda's active time: $$\text{Nanda's time} = 36 - 6 = 30 \text{ months}$$ 2. Establish the ratio of their investments: $$\text{Simran} : \text{Nanda} = (50000 \times 36) : (80000 \times 30)$$ 3. Simplify the ratio by removing four zeros from the capitals: $$\text{Ratio} = (5 \times 36) : (8 \times 30)$$ 4. Simplify further (divide both by $6$): $$\text{Ratio} = (5 \times 6) : (8 \times 5)$$ $$\text{Ratio} = 30 : 40 = 3 : 4$$ 5. Total parts = $3 + 4 = 7$. 6. Calculate Simran's share (3 parts): $$\text{Simran's Share} = 24500 \times \left(\frac{3}{7}\right)$$ $$\text{Simran's Share} = 3500 \times 3 = 10500$$ 7. Compare with options. ₹ $10500$ is not listed among (a), (b), (c), or (d). ### Exam Strategy & Shortcut Simplify $(5 \times 36) : (8 \times 30)$ quickly by noting $36/30 = 6/5$. Thus the ratio is $5 \times 6 : 8 \times 5 \implies 30:40 \implies 3:4$. Knowing the total parts is $7$, $24500/7 = 3500$. Simran's share is $3500 \times 3 = 10500$. Since $10500$ is missing, immediately mark "None of these" without second-guessing. ### Common Pitfall A common mistake is forcing an answer. Students might arrive at $10500$, see $10250$ in the options, assume they made a small arithmetic error, and mark the wrong option instead of confidently selecting "None of these". ### Final Answer Therefore, the correct answer is **None of these**.