`Rs. 260200` is divided between Ram and Shyam so that the amount that Ram receives in 4 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram's share is

Options

A. `Rs. 125000`
B. `Rs. 135200 `
C. `Rs.152000`
D. `Rs. 108200`

Answer

To solve the problem, we need to determine how much money Ram receives from the total amount of Rs. 260200, given that the amount he receives in 4 years is equal to the amount Shyam receives in 6 years at a compounded interest rate of 4% per annum.

### Step-by-Step Solution:

1. **Understand the Problem**:
We know that Ram's amount after 4 years is equal to Shyam's amount after 6 years, and the interest is compounded annually at 4%.

2. **Use the Compound Interest Formula**:
The formula for the amount \( A \) after \( t \) years with principal \( P \) at rate \( r \) is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Here, \( r = 4\% \).

3. **Set Up the Equations**:
Let Ram's principal amount be \( P_R \) and Shyam's principal amount be \( P_S \).
- For Ram after 4 years:
\[ A_R = P_R \left(1 + \frac{4}{100}\right)^4 = P_R \left(1.04\right)^4 \]
- For Shyam after 6 years:
\[ A_S = P_S \left(1 + \frac{4}{100}\right)^6 = P_S \left(1.04\right)^6 \]
Since \( A_R = A_S \), we have:
\[ P_R \left(1.04\right)^4 = P_S \left(1.04\right)^6 \]

4. **Simplify the Equation**:
Dividing both sides by \( \left(1.04\right)^4 \):
\[ P_R = P_S \left(1.04\right)^2 \]
This means:
\[ P_R = P_S \cdot 1.0816 \]

5. **Express Total Amount**:
The total amount shared between Ram and Shyam is:
\[ P_R + P_S = 260200 \]
Substituting \( P_R \):
\[ P_S \cdot 1.0816 + P_S = 260200 \]
\[ P_S (1.0816 + 1) = 260200 \]
\[ P_S \cdot 2.0816 = 260200 \]

6. **Calculate Shyam's Principal**:
\[ P_S = \frac{260200}{2.0816} \approx 125,000 \]

7. **Calculate Ram's Principal**:
Now substituting back to find \( P_R \):
\[ P_R = 1.0816 \cdot P_S = 1.0816 \cdot 125000 \approx 135200 \]

### Final Answer:
Ram's share is approximately **Rs. 135200**.