A sum of Rs 10000 amounts to 12200 in 2 years and Rs 13300 in 3 years at simple interest. Find the rate of interest

Options

A. A)`10%`
B. B)`11%`
C. C)`12%`
D. D)`22%`

Answer

To solve the problem step by step, we will use the information given about the principal amount, the amounts after 2 years and 3 years, and the formula for simple interest.

### Step 1: Identify the given values
- Principal (P) = Rs 10,000
- Amount after 2 years (A2) = Rs 12,200
- Amount after 3 years (A3) = Rs 13,300

### Step 2: Calculate the interest for 2 years
The interest earned over 2 years can be calculated using the formula:
\[ \text{Interest (I)} = \text{Amount (A)} - \text{Principal (P)} \]

For 2 years:
\[ I_2 = A_2 - P = 12,200 - 10,000 = 2,200 \]

### Step 3: Calculate the interest for 1 year
Since the interest is simple interest, the interest earned each year is the same. Therefore, the interest for 1 year (I) can be calculated as:
\[ I = \frac{I_2}{2} = \frac{2,200}{2} = 1,100 \]

### Step 4: Calculate the rate of interest
The rate of interest (R) can be found using the formula:
\[ R = \left( \frac{\text{Interest (I)}}{\text{Principal (P)}} \right) \times 100 \]

Substituting the values:
\[ R = \left( \frac{1,100}{10,000} \right) \times 100 = 11\% \]

### Conclusion
The rate of interest is 11%.