Net settlement by present worth comparison: A owes B Rs. 1120 payable 2 years hence, and B owes A Rs. 1081.50 payable 6 months hence. They decide to settle immediately at a 6% per annum simple-interest basis. Who should pay and how much?

Introduction / Context:When two parties owe each other different future-dated amounts, the fair immediate settlement uses present worth (true-discount method) at the given simple-interest rate for each liability. Net the present worths to decide the direction and magnitude of payment.

Given Data / Assumptions:

• A → B: 1120 due in 2 years.
• B → A: 1081.50 due in 6 months.
• Rate r = 6% p.a. simple.
• Present worth PW = A / (1 + r * t).

Concept / Approach:Compute PW of each future payment to “now.” The party whose PW-liability is larger should pay the difference to square accounts today.

Step-by-Step Solution:PW(A’s liability) = 1120 / (1 + 0.06 * 2) = 1120 / 1.12 = 1000.PW(B’s liability) = 1081.50 / (1 + 0.06 * 0.5) = 1081.50 / 1.03 = 1050.Net = 1050 − 1000 = 50 in favor of A (since B’s present liability is higher).Therefore, B should pay A Rs. 50.

Verification / Alternative check:Forward check: If A receives Rs. 50 now, the present values balance at this rate. Accruing both PWs to a common future date also yields equal totals, confirming fairness.

Why Other Options Are Wrong:

• “A Rs. 50/70” invert the direction.
• “B Rs. 70” overstates the net difference.

Common Pitfalls:

• Discounting both for the full two years, or forgetting 6 months for B’s debt.
• Using banker’s discount instead of present-worth division.

Final Answer:B Rs. 50