Mohan lent some amount of money at `9%` simple interest and an equal amount of money at `10%` simple interest each for 2 years. If his total interest was Rs. 760, what amount was lent in each case ?

Options

A. Rs. 1700
B. Rs. 1800
C. Rs. 1900
D. Rs. 2000

Answer

To solve the problem step by step, we will use the formula for simple interest, which is:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (the amount lent)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 1: Define the variables
Let the amount lent at 9% be \( P \). Since he lent an equal amount at 10%, the amount lent at 10% is also \( P \).

### Step 2: Calculate the simple interest for both amounts
1. **For the amount lent at 9%:**
\[ \text{SI}_{9\%} = \frac{P \times 9 \times 2}{100} = \frac{18P}{100} = 0.18P \]

2. **For the amount lent at 10%:**
\[ \text{SI}_{10\%} = \frac{P \times 10 \times 2}{100} = \frac{20P}{100} = 0.20P \]

### Step 3: Set up the equation for total interest
According to the problem, the total interest from both amounts is Rs. 760. Therefore, we can set up the equation:
\[ \text{SI}_{9\%} + \text{SI}_{10\%} = 760 \]
Substituting the values we calculated:
\[ 0.18P + 0.20P = 760 \]

### Step 4: Combine like terms
\[ 0.38P = 760 \]

### Step 5: Solve for \( P \)
To find \( P \), divide both sides by 0.38:
\[ P = \frac{760}{0.38} \]
Calculating this gives:
\[ P = 2000 \]

### Step 6: Conclusion
The amount lent in each case is Rs. 2000.