Raj and Prithvi both start a business together in which Raj invests Rs X and Prithvi invests Rs (X + 2000). At the end of one year, the total profit earned was ₹8400,of which Raj’s share was ₹3600. How much had Prithvi invested in the business?

Options

A. ₹ 16400
B. ₹ 12000
C. ₹ 125000
D. ₹ 8000

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the Investments**:
- Raj's investment = Rs X
- Prithvi's investment = Rs (X + 2000)

2. **Total Profit Calculation**:
- Total profit earned = Rs 8400
- Raj's share of the profit = Rs 3600
- Therefore, Prithvi's share of the profit = Total profit - Raj's share = 8400 - 3600 = Rs 4800

3. **Profit Sharing Ratio**:
- Raj's share = Rs 3600
- Prithvi's share = Rs 4800
- The ratio of their shares = Raj's share : Prithvi's share = 3600 : 4800
- Simplifying this ratio gives us 3 : 4.

4. **Investment Ratio**:
- Since profit is proportional to investment, we can set up the equation:
- Let the time period for both investments be the same (1 year).
- Therefore, we can write the equation based on the ratio of their investments:
\[ \frac{Raj's\ Investment}{Prithvi's\ Investment} = \frac{3}{4} \]
- Substituting the investments:
\[ \frac{X}{X + 2000} = \frac{3}{4} \]

5. **Cross Multiplication**:
- Cross multiplying gives us:
\[ 4X = 3(X + 2000) \]

6. **Expand and Solve for X**:
- Expanding the right side:
\[ 4X = 3X + 6000 \]
- Rearranging gives:
\[ 4X - 3X = 6000 \]
\[ X = 6000 \]

7. **Calculate Prithvi's Investment**:
- Prithvi's investment = X + 2000 = 6000 + 2000 = Rs 8000.

Thus, Prithvi had invested Rs 8000 in the business.