Kamal and Anand each 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 .

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the variables
Let the amount of money lent by both Kamal and Anand be denoted as \( x \).

### Step 2: Calculate Simple Interest for Kamal
The formula for Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (which is \( x \))
- \( R \) = Rate of interest (5%)
- \( T \) = Time (2 years)

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

### Step 3: Calculate Compound Interest for Anand
The formula for Compound Interest (CI) is given by:
\[ \text{Amount} = P \left(1 + \frac{R}{100}\right)^T \]
So, the amount for Anand is:
\[ \text{Amount} = x \left(1 + \frac{5}{100}\right)^2 = x \left(1 + 0.05\right)^2 = x \left(1.05\right)^2 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Thus, the amount becomes:
\[ \text{Amount} = 1.1025x \]
The Compound Interest (CI) is then calculated as:
\[ \text{CI} = \text{Amount} - P = 1.1025x - x = 0.1025x \]

### Step 4: Set up the equation based on the difference
According to the problem, Anand received Rs 15 more than Kamal:
\[ \text{CI} - \text{SI} = 15 \]
Substituting the values we calculated:
\[ 0.1025x - \frac{x}{10} = 15 \]
To simplify, convert \( \frac{x}{10} \) to a decimal:
\[ 0.1025x - 0.1x = 15 \]
This simplifies to:
\[ 0.0025x = 15 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by \( 0.0025 \):
\[ x = \frac{15}{0.0025} = 6000 \]

### Conclusion
Thus, the amount of money lent by each, Kamal and Anand, is Rs 6000.

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