On a certain sum, the difference between the compound interest and the simple interest for the second year is ₹3,600 and the same for the third year is ₹7,740. What is the sum? (Assume that in case of compound interest, compounding is done annually.)

To solve this problem, we need to understand the difference between compound interest and simple interest.

The difference between the compound interest and the simple interest for the second year is the simple interest for the first year.

The difference between the compound interest and the simple interest for the third year is the simple interest for the first year plus the simple interest for the second year.

Given that the difference for the second year is ₹3,600 and for the third year is ₹7,740, we can set up the following equation:

Simple Interest for the first year + Simple Interest for the second year = ₹7,740

Since the simple interest for the first year is ₹3,600 (the difference for the second year), we can substitute this into the equation:

₹3,600 + Simple Interest for the second year = ₹7,740

Solving for the Simple Interest for the second year, we get:

Simple Interest for the second year = ₹7,740 - ₹3,600 = ₹4,140

Since the simple interest is the same for every year, the simple interest for the first year (₹3,600) should be equal to the simple interest for the second year (₹4,140). But they are not equal, which means there is a mistake in the problem or it's a trick question.

In a normal scenario, if the simple interests were equal, we could use the formula for simple interest to find the sum:

Simple Interest = (Principal Amount * Rate * Time) / 100

And solve for the Principal Amount. But in this case, it's not possible due to the discrepancy in the simple interests for the first and second years.

To solve this problem, we need to understand the difference between compound interest and simple interest.

The difference between the compound interest and the simple interest for the second year is the simple interest for the first year.

So, the simple interest for the first year is ₹3,600.

The difference between the compound interest and the simple interest for the third year is the simple interest for the first year plus the interest on the simple interest for the first year.

So, ₹7,740 (the difference for the third year) = ₹3,600 (the simple interest for the first year) + the interest on ₹3,600.

Therefore, the interest on ₹3,600 is ₹7,740 - ₹3,600 = ₹4,140.

Since the interest is compounded annually, the rate of interest is (₹4,140/₹3,600) * 100 = 115%.

Now, we know that the simple interest for the first year is ₹3,600.

So, the sum (or principal) is (₹3,600/115) * 100 = ₹3,130.43 approximately.

Therefore, the sum is approximately ₹3,130.43.