Ramesh borrowed a sum at 5 per annum simple interset from Rahul, He recturns the amount after 5 years. Rahul returns 2% of the total amount received. How much did Ramesh borrowed if he received Rs. 5 ?

Options

A. Rs. 250
B. Rs. 200
C. Rs. 150
D. Rs. 175

Answer

To solve the problem step by step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Understand the given information
- Ramesh borrowed a sum of money (let's call it \( P \)).
- The interest rate is 5% per annum.
- The time period for which the money is borrowed is 5 years.
- After 5 years, Ramesh returns the amount, and Rahul returns 2% of the total amount received from Ramesh.
- Ramesh received Rs. 5 from Rahul after the return.

### Step 2: Calculate the Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the amount borrowed)
- \( R \) = Rate of interest (5% per annum)
- \( T \) = Time (5 years)

Substituting the values into the formula:
\[ SI = \frac{P \times 5 \times 5}{100} = \frac{25P}{100} = \frac{P}{4} \]

### Step 3: Calculate the Total Amount Returned
The total amount \( A \) that Ramesh returns after 5 years is the sum of the principal and the simple interest:
\[ A = P + SI = P + \frac{P}{4} = \frac{4P}{4} + \frac{P}{4} = \frac{5P}{4} \]

### Step 4: Calculate the Amount Returned to Ramesh
According to the problem, Rahul returns 2% of the total amount received from Ramesh:
\[ \text{Amount returned to Ramesh} = 2\% \text{ of } A = \frac{2}{100} \times \frac{5P}{4} = \frac{5P}{200} \]

### Step 5: Set up the equation
We know from the problem that the amount returned to Ramesh is Rs. 5:
\[ \frac{5P}{200} = 5 \]

### Step 6: Solve for \( P \)
Cross-multiplying gives:
\[ 5P = 5 \times 200 \]
\[ 5P = 1000 \]
Dividing both sides by 5:
\[ P = \frac{1000}{5} = 200 \]

### Conclusion
Thus, the amount that Ramesh borrowed is Rs. 200.

### Final Answer
The correct option is B - 200.

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