Divide `3600` into two parts such that if one part is lent at `9%` p.a. and the other at `10%` per annum the total income from interest is `333`.

Options

A. `"₹2900, ₹900"`
B. `"₹2500, ₹750"`
C. `"₹1700, ₹700"`
D. `"₹2700, ₹900"`

Answer

To solve the problem of dividing `3600` into two parts such that one part is lent at `9%` per annum and the other at `10%` per annum, resulting in a total interest of `333`, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Parts**:
Let one part be `p`. Therefore, the other part will be `3600 - p`.

2. **Calculate Simple Interest for Each Part**:
- For the part lent at `9%`, the simple interest (SI1) can be calculated as:
\[ SI1 = p \times \frac{9}{100} \times 1 = \frac{9p}{100} \]
- For the part lent at `10%`, the simple interest (SI2) can be calculated as:
\[ SI2 = (3600 - p) \times \frac{10}{100} \times 1 = \frac{10(3600 - p)}{100} = \frac{36000 - 10p}{100} \]

3. **Set Up the Equation for Total Interest**:
According to the problem, the total interest from both parts is `333`. Therefore, we can write:
\[ SI1 + SI2 = 333 \]
Substituting the expressions for SI1 and SI2:
\[ \frac{9p}{100} + \frac{36000 - 10p}{100} = 333 \]

4. **Multiply Through by 100 to Eliminate the Denominator**:
\[ 9p + 36000 - 10p = 33300 \]

5. **Combine Like Terms**:
\[ -p + 36000 = 33300 \]

6. **Isolate `p`**:
\[ -p = 33300 - 36000 \]
\[ -p = -2700 \]
\[ p = 2700 \]

7. **Calculate the Other Part**:
The other part is:
\[ 3600 - p = 3600 - 2700 = 900 \]

8. **Final Answer**:
Therefore, the two parts are:
- One part: `2700`
- Other part: `900`

### Summary:
- The amount lent at `9%` is `2700`.
- The amount lent at `10%` is `900`.