A sum of Rs. 1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is:

Options

A. Rs. 500
B. Rs. 1000
C. Rs. 750
D. Rs. 1250

Answer

To solve the problem, we need to determine how much of the Rs. 1500 is lent out at 12.5% interest. Let's denote:

- The amount lent at 10% as \( x \)
- The amount lent at 12.5% as \( 1500 - x \)

### Step 1: Calculate Simple Interest for Both Parts

The formula for simple interest (SI) is given by:

\[ SI = \frac{P \times R \times T}{100} \]

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

For the first part (at 10% for 5 years):
\[ SI_1 = \frac{x \times 10 \times 5}{100} = \frac{50x}{100} = 0.5x \]

For the second part (at 12.5% for 4 years):
\[ SI_2 = \frac{(1500 - x) \times 12.5 \times 4}{100} = \frac{50(1500 - x)}{100} = 0.5(1500 - x) \]

### Step 2: Set the Simple Interests Equal

According to the problem, the simple interest from both parts is equal:
\[ 0.5x = 0.5(1500 - x) \]

### Step 3: Simplify the Equation

We can simplify the equation by multiplying both sides by 2 to eliminate the 0.5:
\[ x = 1500 - x \]

### Step 4: Solve for \( x \)

Now, we can solve for \( x \):
\[ x + x = 1500 \]
\[ 2x = 1500 \]
\[ x = \frac{1500}{2} = 750 \]

### Step 5: Calculate the Amount Lent at 12.5%

Now that we have \( x \), we can find the amount lent at 12.5%:
\[ 1500 - x = 1500 - 750 = 750 \]

Thus, the sum lent out at 12.5% is Rs. 750.

### Final Answer:
The sum lent out at 12.5% is Rs. 750.

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