Ajay takes some loan from Rashmi at the rate of 5% per annum and after 2 yr, Ajay gave back X 8800 to Rashmi and this way paid his whole loan. Find the interest paid by Ajay.

Options

A. X825
B. X957
C. X800
D. X850

Answer

To solve the problem step by step, we will follow the process of calculating the principal amount, the interest paid, and finally, the total interest paid by Ajay.

### Step 1: Identify the given values
- Rate of interest (R) = 5% per annum
- Time (T) = 2 years
- Total amount paid back (A) = ₹8800

### Step 2: Set up the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

### Step 3: Express the total amount in terms of Principal and Interest
The total amount paid back (A) is the sum of the principal and the interest:
\[ A = P + SI \]
Substituting the formula for SI into this equation gives:
\[ 8800 = P + \frac{P \times 5 \times 2}{100} \]

### Step 4: Simplify the equation
First, calculate the interest:
\[ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]
Now substitute this back into the total amount equation:
\[ 8800 = P + \frac{P}{10} \]
To combine the terms, find a common denominator:
\[ 8800 = \frac{10P}{10} + \frac{P}{10} = \frac{11P}{10} \]

### Step 5: Solve for Principal (P)
To isolate \( P \), multiply both sides by 10:
\[ 8800 \times 10 = 11P \]
\[ 88000 = 11P \]
Now divide both sides by 11:
\[ P = \frac{88000}{11} \]
Calculating this gives:
\[ P = 8000 \]

### Step 6: Calculate the Simple Interest (SI)
Now that we have the principal, we can calculate the interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{8000 \times 5 \times 2}{100} \]
Calculating this gives:
\[ SI = \frac{80000}{100} = 800 \]

### Step 7: Conclusion
The interest paid by Ajay is ₹800.