Simple Interest

Step 1: Calculate the compound interest (CI) earned by Aman. The formula for the amount A is . Aman's Amount = . Aman's Interest = Amount - Principal = .

Step 2: Calculate the simple interest (SI) earned by Ajay. The formula for Simple Interest is . Ajay's Interest = .

Step 3: Equate the two interests and solve for P. Given that the interests are the same: The sum invested by Aman (P) is Rs.50,000.

Step 1: Define the variables for the two parts of the principal. Let the first part (lent at 10%) be and the second part (lent at 8%) be . We know that .

Step 2: Set up the interest equality based on the given condition. The formula for Simple Interest is . Interest on the first part: . Interest on the second part: . Given , we have:

Step 3: Find the ratio between the two principals. So, the money was lent in the ratio .

Step 4: Calculate the value of the first part, . The total number of parts in the ratio is . The sum lent at 10% ( ) corresponds to 32 parts of the total. Note: The numbers seem inconsistent. However, if we assume the total sum was meant to be Rs.57,000 for the ratio to work out cleanly, then . Given the options, this is the intended logic.