A man invested an amount at 12 % per annum simple interest and another amount at 10 % per annum simpel interest. He received an annual interest fo ₹ 2600. But, if he had intercharged the amounts invested, he would havr received ₹ 140 less. What amounts did he invest at the different rates ?

Explanation

To solve the problem, we need to set up equations based on the information given. Let's denote the amounts invested at 12% and 10% as \( x \) and \( y \) respectively.

### Step 1: Setting up the equations
1. The total interest received from both investments is ₹2600.
- The interest from the amount invested at 12% is \( \frac{12}{100} \times x \).
- The interest from the amount invested at 10% is \( \frac{10}{100} \times y \).
- Therefore, we can write the first equation as:
\[
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