Find the borrowed sum that was paid in the two annual installments of Rs. 216 each, if the rate of CI is 20%20% pa.

Sure, here is the step by step solution:

Step 1: We know that the amount paid in the first year is Rs. 216. This includes the principal and the interest for the first year. Let's denote the principal (the borrowed sum) as P.

Step 2: The interest for the first year is 20% of the principal. So, the principal plus the interest is P + 0.20P = 1.20P.

Step 3: We know that 1.20P = Rs. 216. So, we can solve this equation for P. P = Rs. 216 / 1.20 = Rs. 180.

Step 4: The amount paid in the second year is also Rs. 216. This includes the principal and the interest for the second year. The interest for the second year is 20% of the principal remaining after the first year's payment.

Step 5: The principal remaining after the first year's payment is P - Rs. 180 = Rs. 180 - Rs. 180 = Rs. 0.

Step 6: The interest for the second year is 20% of Rs. 0 = Rs. 0.

Step 7: So, the total amount paid in the second year is the principal remaining after the first year's payment plus the interest for the second year = Rs. 0 + Rs. 0 = Rs. 0.

Step 8: But we know that the amount paid in the second year is Rs. 216. So, there is a contradiction. This means that our assumption that the principal is Rs. 180 is incorrect.

Step 9: Therefore, the borrowed sum cannot be determined from the given information.