Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev's share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999 ?

Options

A. Rs. 45,000
B. Rs. 50,000
C. Rs. 70,000
D. Rs. 75,000

Answer

To solve the problem step by step, we will calculate the investments made by each partner and then determine Rajeev's share in the profit.

### Step 1: Calculate Shekhar's Total Investment
- In 1999, Shekhar invested Rs. 25,000.
- In 2000, he invested an additional Rs. 10,000.
- In 2001, he invested another Rs. 10,000.

**Total Investment by Shekhar:**
\[ \text{Total Investment} = 25000 + 10000 + 10000 = 45000 \text{ (for 3 years)} \]
- Shekhar's investment is considered for the duration of each year:
- 1999: Rs. 25,000 for 3 years = \( 25000 \times 3 = 75000 \)
- 2000: Rs. 10,000 for 2 years = \( 10000 \times 2 = 20000 \)
- 2001: Rs. 10,000 for 1 year = \( 10000 \times 1 = 10000 \)

**Total Contribution of Shekhar:**
\[ 75000 + 20000 + 10000 = 105000 \]

### Step 2: Calculate Rajeev's Total Investment
- Rajeev joined in 2000 with Rs. 35,000 and remained for 2 years.

**Total Investment by Rajeev:**
\[ \text{Total Investment} = 35000 \text{ (for 2 years)} \]
- Rajeev's investment is considered for the duration of each year:
- 2000: Rs. 35,000 for 2 years = \( 35000 \times 2 = 70000 \)

### Step 3: Calculate Jatin's Total Investment
- Jatin joined in 2001 with Rs. 35,000 and remained for 1 year.

**Total Investment by Jatin:**
\[ \text{Total Investment} = 35000 \text{ (for 1 year)} \]
- Jatin's investment is considered for the duration of each year:
- 2001: Rs. 35,000 for 1 year = \( 35000 \times 1 = 35000 \)

### Step 4: Calculate Total Investment of All Partners
**Total Investment:**
\[ \text{Total Investment} = \text{Shekhar's Total} + \text{Rajeev's Total} + \text{Jatin's Total} \]
\[ = 105000 + 70000 + 35000 = 210000 \]

### Step 5: Calculate Rajeev's Share in the Profit
- Total profit earned = Rs. 1,50,000.

**Rajeev's Share:**
\[ \text{Rajeev's Share} = \left( \frac{\text{Rajeev's Contribution}}{\text{Total Investment}} \right) \times \text{Total Profit} \]
\[ = \left( \frac{70000}{210000} \right) \times 150000 \]
\[ = \frac{1}{3} \times 150000 = 50000 \]

### Final Answer
Rajeev's share in the profit is Rs. 50,000.

---