Avinash lends Rs. 5400 to Rajeev at a simple interest rate of 8% per annum for 4 years. Rajeev, in turn, lends the same Rs. 5400 to Chanukya at a simple interest rate of 6% per annum for 4 years. At the end of 4 years, how much extra amount, in rupees, must Rajeev pay out of his own pocket to fully settle what he owes Avinash?

Introduction / Context:
This problem is a chain-lending simple interest question that compares the interest Rajeev has to pay to Avinash with the interest Rajeev receives from Chanukya. Because Rajeev borrows and lends the same amount for the same time period but at different rates of interest, he will either gain or lose money based on the spread between the two rates.

Given Data / Assumptions:

• Principal amount in both transactions P = Rs. 5400.
• Avinash lends to Rajeev at R1 = 8% per annum simple interest for T = 4 years.
• Rajeev lends to Chanukya at R2 = 6% per annum simple interest for the same T = 4 years.
• Simple interest formula: SI = (P * R * T) / 100.
• We want the extra amount Rajeev must pay from his own pocket at the end of 4 years.

Concept / Approach:
Since both loans have the same principal and duration, the difference in total interest is purely due to the difference in rates. Rajeev pays interest at 8% but earns at 6%. The shortfall in interest is exactly what he must add from his own money in order to pay Avinash the full amount due.

Step-by-Step Solution:
Interest Rajeev must pay Avinash: SI1 = (5400 * 8 * 4) / 100. Compute SI1: 5400 * 8 = 43200; 43200 * 4 = 172800; SI1 = 172800 / 100 = Rs. 1728. Interest Rajeev receives from Chanukya: SI2 = (5400 * 6 * 4) / 100. Compute SI2: 5400 * 6 = 32400; 32400 * 4 = 129600; SI2 = 129600 / 100 = Rs. 1296. Difference in interest: SI1 - SI2 = 1728 - 1296 = Rs. 432. Thus, Rajeev is short by Rs. 432 and must pay this amount himself.
Verification / Alternative check:
Total amount Avinash expects after 4 years = 5400 + 1728 = Rs. 7128. Total amount Chanukya pays to Rajeev = 5400 + 1296 = Rs. 6696. The gap is 7128 - 6696 = Rs. 432, exactly the extra amount Rajeev must contribute, confirming the result.

Why Other Options Are Wrong:
Rs. 364, Rs. 410, Rs. 498, and Rs. 540 do not equal the difference between the two simple interest amounts. Using any of these values would imply an incorrect spread between 8% and 6% over 4 years on Rs. 5400 and would not balance the total required and received amounts.

Common Pitfalls:
A frequent error is to calculate only one side of the transaction or to subtract the rates 8% and 6% but forget to multiply by both principal and time. Some students mistakenly compare only yearly interests and forget to scale by 4 years, while others confuse simple and compound interest formulas.

Final Answer:
Rajeev must pay an extra Rs. 432 from his own pocket.