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Let's solve this step-by-step.

1. Let Radhika's total salary be represented by \( x \).

2. She spends:
   - \(\frac{1}{2}\) of her salary on installments, so the amount spent on installments is \( \frac{1}{2}x \).
   - \(\frac{1}{3}\) of her salary on conveyance, so the amount spent on conveyance is \( \frac{1}{3}x \).
   - Additionally, she donates 500 rupees.

3. According to the problem, after all these expenses, she is left with 10,000 rupees. This can be expressed in an equation as:
   \[
   x - \left(\frac{1}{2}x + \frac{1}{3}x + 500\right) = 10000
   \]

4. Simplify the equation:
   \[
   x - \frac{1}{2}x - \frac{1}{3}x - 500 = 10000
   \]

5. Combine like terms. The terms involving \( x \) can be rewritten as:
   \[
   x \left(1 - \frac{1}{2} - \frac{1}{3}\right) = 10000 + 500
   \]

6. Calculate \(1 - \frac{1}{2} - \frac{1}{3}\):
   - First, find a common denominator:
     \[
     1 = \frac{6}{6}, \quad \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
     \]
   - Then, substitute these values:
     \[
     1 - \frac{1}{2} - \frac{1}{3} = \frac{6 - 3 - 2}{6} = \frac{1}{6}
     \]

7. Substitute back into the equation:
   \[
   x \cdot \frac{1}{6} = 10500
   \]
   \[
   x = 10500 \times 6
   \]
   \[
   x = 63000
   \]

So, Radhika's salary is **63,000 rupees**.

8. To find out how much she spent on installments:
   \[
   \text{Installments} = \frac{1}{2} \times 63000 = 31500
   \]

### Final Answer:
- **Radhika's salary**: 63,000 rupees
- **Amount spent on installments**: 31,500 rupees

Would you like further details or have any questions?

Here are some related questions to expand this problem:

1. What would be her remaining amount if her salary was 70,000 rupees instead?
2. How much would she save if she reduced her conveyance expenses to \( \frac{1}{4} \) of her salary?
3. If her donation increased to 1,000 rupees, how would her remaining amount change?
4. How would the answer change if she was left with only 8,000 rupees instead of 10,000?
5. What fraction of her salary did she donate as per the initial problem?

**Tip:** When dealing with word problems, it’s helpful to clearly define variables and set up an equation that reflects the given conditions.

Radhika spent 1/2 of her salary paying installments, 1/3 on conveyance, and gave ₹500 as a donation. If she is left with ₹10,000, how much is her salary and how much did she spend on installments?

Learn how to calculate Radhika's total salary given her expenses on installments, conveyance, and a donation, along with the amount left. This solution involves solving linear equations and working with fractions, suitable for students in Grades 8-10.

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