A man borrowed a sum of Rs. 1000 and after two years he returned Rs. 1200. Calculate the rate of interest which he paid for the sum?

Options

A. `5%`
B. `10%`
C. `12 1/2%`
D. `15%`

Answer

To find the rate of interest paid by the man who borrowed Rs. 1000 and returned Rs. 1200 after two years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 1000
- Amount (A) = Rs. 1200
- Time (T) = 2 years

### Step 2: Calculate the interest (I)
To find the interest, we subtract the principal from the amount returned:
\[ I = A - P \]
\[ I = 1200 - 1000 = 200 \text{ Rs.} \]

### Step 3: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- I = Interest
- P = Principal
- R = Rate of interest
- T = Time in years

### Step 4: Substitute the known values into the formula
We can substitute the values we have into the formula:
\[ 200 = \frac{1000 \times R \times 2}{100} \]

### Step 5: Simplify the equation
First, we can simplify the right side:
\[ 200 = \frac{2000R}{100} \]
\[ 200 = 20R \]

### Step 6: Solve for R
To find R, divide both sides by 20:
\[ R = \frac{200}{20} \]
\[ R = 10 \]

### Conclusion
The rate of interest is \( R = 10\% \).

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