Divide `₹1550` into two parts such that if one part is lent out at `15%` p.a. and the other at `24%` per annum, the total yearly interest income is `₹300`.

Answer

To solve the problem of dividing ₹1550 into two parts such that one part is lent out at 15% per annum and the other at 24% per annum, resulting in a total yearly interest income of ₹300, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables:**
Let one part be \( x \). Then, the other part will be \( 1550 - x \).

2. **Calculate the Interest for Each Part:**
- The interest for the first part (lent at 15% per annum) can be calculated using the formula for simple interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
For the first part:
\[ \text{Interest}_1 = \frac{x \times 15 \times 1}{100} = \frac{15x}{100} \]

- The interest for the second part (lent at 24% per annum):
\[ \text{Interest}_2 = \frac{(1550 - x) \times 24 \times 1}{100} = \frac{24(1550 - x)}{100} \]

3. **Set Up the Equation:**
According to the problem, the total interest from both parts is ₹300:
\[ \frac{15x}{100} + \frac{24(1550 - x)}{100} = 300 \]

4. **Clear the Denominator:**
Multiply the entire equation by 100 to eliminate the fractions:
\[ 15x + 24(1550 - x) = 30000 \]

5. **Expand and Simplify:**
Expand the equation:
\[ 15x + 37200 - 24x = 30000 \]
Combine like terms:
\[ -9x + 37200 = 30000 \]

6. **Isolate \( x \):**
Subtract 37200 from both sides:
\[ -9x = 30000 - 37200 \]
\[ -9x = -7200 \]
Divide by -9:
\[ x = 800 \]

7. **Find the Other Part:**
Now, substitute \( x \) back to find the other part:
\[ 1550 - x = 1550 - 800 = 750 \]

### Final Answer:
The two parts are ₹800 and ₹750.

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