Kamal and Anand cach lent the same sum of money for 2 years at 5% at simple interest and compound interest respectively. Anand received Rs 15 more than Kamal. Find the amount of money lent by each and the interest received.

Answer

To solve the problem step by step, we will find the amount of money lent by Kamal and Anand, as well as the interest received by each of them.

### Step 1: Define the variables
Let the principal amount lent by both Kamal and Anand be \( P \).

### Step 2: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times r \times t}{100} \]
Where:
- \( r = 5\% \) (rate of interest)
- \( t = 2 \) years

Substituting the values:
\[ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]

### Step 3: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( A \) is the total amount after \( t \) years
- \( r = 5\% \)
- \( t = 2 \)

Calculating the amount \( A \):
\[ A = P \left(1 + \frac{5}{100}\right)^2 = P \left(1 + 0.05\right)^2 = P \left(1.05\right)^2 = P \times 1.1025 \]
Now, the Compound Interest (CI) is:
\[ CI = A - P = P \times 1.1025 - P = P(1.1025 - 1) = P \times 0.1025 \]

### Step 4: Set up the equation based on the problem statement
According to the problem, Anand received Rs 15 more than Kamal:
\[ CI - SI = 15 \]
Substituting the values we found:
\[ P \times 0.1025 - \frac{P}{10} = 15 \]

### Step 5: Simplify the equation
First, convert \(\frac{P}{10}\) to a decimal:
\[ \frac{P}{10} = 0.1P \]
Now, substituting this into the equation:
\[ P \times 0.1025 - 0.1P = 15 \]
This simplifies to:
\[ P(0.1025 - 0.1) = 15 \]
Calculating \(0.1025 - 0.1\):
\[ P \times 0.0025 = 15 \]

### Step 6: Solve for \( P \)
Now, divide both sides by \(0.0025\):
\[ P = \frac{15}{0.0025} = 6000 \]

### Step 7: Calculate the interest received by Kamal and Anand
Now that we have \( P = 6000 \):
- **Simple Interest (SI)**:
\[ SI = \frac{6000}{10} = 600 \]
- **Compound Interest (CI)**:
\[ CI = 6000 \times 0.1025 = 615 \]

### Final Results
- Amount lent by each: Rs 6000
- Interest received by Kamal: Rs 600
- Interest received by Anand: Rs 615