A owes B, ₹ 1573 payable $1\frac{1}{2}$ years hence. Also B owes A, ₹ 1444.50 payable 6 months hence. If they want to settle the account forthwith, keeping 14% as the rate of interest, then who should pay and how much? (a) A, ₹ 28.50 (b) B, ₹ 37.50 (c) A, ₹ 50 (d) B, ₹ 50

### Concept & Present Worth Settle To settle future debts "forthwith" (immediately), we must calculate the Present Worth (PW) of both debts today and find the net difference. $$ \text{PW} = \frac{100 \times \text{Amount}}{100 + (R \times T)} $$ ### Step-by-Step Solution - **A's debt to B:** Amount = ₹ 1573, Time = $1\frac{1}{2} = 1.5$ years, Rate = 14%. $$ \text{PW}_A = \frac{1573 \times 100}{100 + (14 \times 1.5)} = \frac{157300}{100 + 21} = \frac{157300}{121} = 1300 $$ A presently owes B ₹ 1300. - **B's debt to A:** Amount = ₹ 1444.50, Time = 6 months = 0.5 years, Rate = 14%. $$ \text{PW}_B = \frac{1444.50 \times 100}{100 + (14 \times 0.5)} = \frac{144450}{100 + 7} = \frac{144450}{107} = 1350 $$ B presently owes A ₹ 1350. - **Net Settlement:** Since B owes A ₹ 1350 and A owes B ₹ 1300, the net amount is $1350 - 1300 = 50$. B must pay A ₹ 50 to settle the account. ### Exam Strategy & Shortcut Always bring all obligations to $t=0$ (Present Worth). The calculations are designed to be clean multiples. $1573$ is a known multiple of $121$ ($13 \times 121 = 1573$), and $144450 / 107$ ends in $50$. Quickly identifying these multiples saves calculation time. ### Common Pitfall Calculating the interest on the final amounts rather than finding the present worth, or netting the future amounts directly without discounting them to the present day. ### Final Answer Therefore, the correct answer is **(d) B, ₹ 50**.