The difference of simple interest of 13% per annum and 12% per annum of a sum in 1 yr is Rs. 110. Then, the sum is

Options

A. ₹ 12000
B. ₹ 13000
C. ₹ 11000
D. ₹ 16000

Answer

To solve the problem, we need to find the principal sum (P) based on the difference in simple interest at two different rates of interest (13% and 12%) over a period of 1 year.

### Step-by-Step Solution:

1. **Understand the Formula for Simple Interest (SI)**:
The formula for simple interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Calculate Simple Interest for 13%**:
For a rate of 13% per annum for 1 year, the simple interest (SI1) can be calculated as:
\[ SI_1 = \frac{P \times 13 \times 1}{100} = \frac{13P}{100} \]

3. **Calculate Simple Interest for 12%**:
For a rate of 12% per annum for 1 year, the simple interest (SI2) can be calculated as:
\[ SI_2 = \frac{P \times 12 \times 1}{100} = \frac{12P}{100} \]

4. **Find the Difference in Simple Interest**:
According to the problem, the difference between the two simple interests is Rs. 110:
\[ SI_1 - SI_2 = 110 \]
Substituting the values we calculated:
\[ \frac{13P}{100} - \frac{12P}{100} = 110 \]

5. **Simplify the Equation**:
Simplifying the left side:
\[ \frac{13P - 12P}{100} = 110 \]
This simplifies to:
\[ \frac{P}{100} = 110 \]

6. **Solve for Principal (P)**:
To find \( P \), multiply both sides by 100:
\[ P = 110 \times 100 = 11000 \]

### Final Answer:
The sum (principal amount) is Rs. 11,000.

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