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Let's analyze the problem step-by-step.

### Problem Breakdown:

- A person lends out some money at **10% per annum simple interest** and another portion at **8% per annum simple interest**.
- In both cases, the total interest he earns after **6 months** is **₹200**.
- We need to find the total amount that was lent out at **8% per annum**.

### Formula for Simple Interest:
\[
\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
\]
where:
- \(P\) = Principal (amount lent)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step-by-step Solution:

1. **Define Variables:**
   - Let \(x\) be the amount lent at **10%** per annum.
   - Let \(y\) be the amount lent at **8%** per annum.
   - Total interest earned after 6 months is **₹200**.

2. **Calculate Interest Earned for Each Portion:**
   - Interest for amount \(x\) lent at 10% per annum for 6 months:
   \[
   \text{Interest for } x = \frac{x \times 10 \times \frac{1}{2}}{100} = \frac{x \times 10}{200} = \frac{x}{20}
   \]

   - Interest for amount \(y\) lent at 8% per annum for 6 months:
   \[
   \text{Interest for } y = \frac{y \times 8 \times \frac{1}{2}}{100} = \frac{y \times 8}{200} = \frac{y}{25}
   \]

3. **Set Up the Equation:**
   \[
   \frac{x}{20} + \frac{y}{25} = 200
   \]

4. **Solve for One Variable:**
   Multiply the entire equation by 100 to clear the denominators:
   \[
   5x + 4y = 20000
   \]

   To find the possible values of \(y\), we need to consider the options provided in the problem (if any were visible). Assuming there were multiple-choice answers, we'd plug each into the equation to find a matching pair for \(x\) and \(y\).

Would you like to continue with a detailed step-by-step solution for each possible value, or do you have any specific choices provided in the original problem? 

### Related Questions:

1. How would the solution change if the time period was different (e.g., 1 year instead of 6 months)?
2. How does compound interest differ from simple interest in such problems?
3. What if the rates were compounded monthly instead of yearly; how would we approach it?
4. Can we solve this problem graphically by plotting the equation?
5. How can we generalize this problem for any two rates of interest and time periods?

### Tip:
When solving such problems, always keep track of units and ensure that the time period (months or years) matches the interest rate's period.

Ashok lent out some money at 10% per annum simple interest and after 6 months, he gained some amount. He also lent out some amount at a simple interest of 8% per annum for six months. In both the cases, he got ₹200 as interest. Which of these could be the amount that was lent out at 8% per annum?

Solve this simple interest problem where Ashok lent out amounts at 10% and 8% per annum for 6 months. Given the total interest earned was ₹200, determine the amount lent at 8% per annum. Suitable for students in Grades 8-10.

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