A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and Rs. 1,020 after a further period of 5 years. Find the principal.

Sure, let's solve this step by step.

1. We know that the sum amounts to Rs. 720 after 2 years. This means that the principal plus 2 years of interest equals Rs. 720.

2. We also know that the sum amounts to Rs. 1,020 after a further period of 5 years. This means that the principal plus 7 years of interest equals Rs. 1,020.

3. If we subtract the first equation from the second, we get 5 years of interest equals Rs. 300 (because 1,020 - 720 = 300).

4. Therefore, the interest rate per year is Rs. 60 (because 300 / 5 = 60).

5. Now, if we subtract 2 years of interest (2*60 = Rs. 120) from the total amount after 2 years (Rs. 720), we get the principal.

6. So, the principal is Rs. 600 (because 720 - 120 = 600).

Therefore, the principal amount is Rs. 600.