Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two 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:

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

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

### Step 1: Define the variables
Let the amount lent at 9% be \( x \) and the amount lent at 10% also be \( x \) (since it is mentioned that both amounts are equal).

### Step 2: Calculate the interest for both amounts
1. **Interest from the amount lent at 9%:**
\[ \text{Interest}_1 = \frac{x \times 9 \times 2}{100} = \frac{18x}{100} = 0.18x \]

2. **Interest from the amount lent at 10%:**
\[ \text{Interest}_2 = \frac{x \times 10 \times 2}{100} = \frac{20x}{100} = 0.20x \]

### 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:
\[ \text{Interest}_1 + \text{Interest}_2 = 760 \]
Substituting the values we calculated:
\[ 0.18x + 0.20x = 760 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 0.38x = 760 \]

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

### Step 6: Conclusion
Thus, the amount lent in each case is Rs. 2000.

### Summary of the solution:
- Amount lent at 9% = Rs. 2000
- Amount lent at 10% = Rs. 2000