A sum of Rs 1500 is lent out in two parts in such a way that the simple interset 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 left 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 find out how much of the total sum of Rs 1500 is lent out at 12.5% per annum. We know that the simple interest earned on both parts is equal. Let's denote:

- Part lent at 10% for 5 years as \( A \)
- Part lent at 12.5% for 4 years as \( B \)

### Step 1: Set up the equations for simple interest

The formula for simple interest is given by:

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

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

For part \( A \) (at 10% for 5 years):

\[ SI_A = \frac{A \times 10 \times 5}{100} = \frac{50A}{100} = 0.5A \]

For part \( B \) (at 12.5% for 4 years):

\[ SI_B = \frac{B \times 12.5 \times 4}{100} = \frac{50B}{100} = 0.5B \]

### Step 2: Set the simple interests equal

Since the simple interests are equal:

\[ 0.5A = 0.5B \]

This simplifies to:

\[ A = B \]

### Step 3: Use the total amount

We know that the total amount lent out is Rs 1500:

\[ A + B = 1500 \]

Since \( A = B \), we can substitute \( B \) with \( A \):

\[ A + A = 1500 \]
\[ 2A = 1500 \]

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

Dividing both sides by 2:

\[ A = \frac{1500}{2} = 750 \]

### Step 5: Find \( B \)

Since \( A = B \):

\[ B = 750 \]

### Conclusion

The sum lent out at 12.5% is:

\[ \text{Sum lent out at 12.5%} = B = 750 \]

### Final Answer

The sum left lent out at 12.5% is Rs 750.

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