Shekhar started a business investing ₹ 25000 in 2009. In 2010, he invested an additional amount of ₹ 10000 and Rajeev joined him with an amount of ₹ 35000. In 2011, Shekhar invested another additional amount of ₹ 10000 and Jatin joined them with an amount of ₹ 35000. What will be Rajeev's share in the profit of ₹ 150000 earned at the end of 3 years from the start of the business in 2009?

### Concept & Annual Capital Adjustments Treat each year as a separate block for partners whose investments change annually. The total equivalent capital is the sum of the capital deployed during each consecutive year. ### Step-by-Step Solution * **Given:** * Total duration = $3 \text{ years}$ (2009, 2010, 2011) * Total Profit = $₹ 150000$ * **Calculate Equivalent Capital:** * **Shekhar:** * 2009 (1st year): $₹ 25000 \times 1 \text{ year}$ * 2010 (2nd year): $(25000 + 10000) = ₹ 35000 \times 1 \text{ year}$ * 2011 (3rd year): $(35000 + 10000) = ₹ 45000 \times 1 \text{ year}$ * Shekhar Total = $25000 + 35000 + 45000 = 105000$ * **Rajeev:** * Joins in 2010. Remains for 2 years (2010, 2011). * Rajeev Total = $35000 \times 2 = 70000$ * **Jatin:** * Joins in 2011. Remains for 1 year (2011). * Jatin Total = $35000 \times 1 = 35000$ * **Calculate Profit Ratio:** * $\text{Ratio} = 105000 : 70000 : 35000$ * Divide all terms by $35000$: * $\text{Ratio} = 3 : 2 : 1$ * **Calculate Rajeev's Share:** * Sum of ratio parts = $3 + 2 + 1 = 6$ * $\text{Rajeev's Share} = \left(\frac{2}{6}\right) \times 150000$ * $\text{Rajeev's Share} = \left(\frac{1}{3}\right) \times 150000 = ₹ 50000$ ### Exam Strategy & Shortcut Observe the numbers: 25k, 35k, 45k. The base multiples are evident early on. Shekhar = $25 + 35 + 45 = 105$ Rajeev = $35 \times 2 = 70$ Jatin = $35 \times 1 = 35$ The numbers 105, 70, and 35 are all multiples of 35. This immediate simplification gives a $3:2:1$ ratio, which makes calculating shares of $150,000$ trivial (divide by 6). ### Common Pitfall Not adding Shekhar's additional investments cumulatively. He added 10k in 2010 (now 35k) and *another* 10k in 2011. Some might mistakenly calculate 2011 as just 25k + 10k = 35k again. ### Final Answer Therefore, the correct answer is **₹ 50000**.