A owes B Rs. 1120 payable 2 year hence, B owes A Rs. 1081.50 payable 6 months hence. If they decide to settle their accounts forthwith by payment of ready money and the rate of interest be 6% per annum, then who should pay and how much?

Answer

To solve the problem, we need to calculate the present worth of the amounts owed by A to B and B to A, considering the interest rate of 6% per annum.

### Step 1: Calculate the Present Worth of A's Debt to B
A owes B Rs. 1120, which is payable in 2 years. We will use the formula for present worth:

\[ \text{Present Worth} = \frac{100 \times \text{Amount}}{100 + R \times T} \]

Where:
- Amount = Rs. 1120
- R = 6% per annum
- T = 2 years

Substituting the values:

\[ \text{Present Worth of A's Debt} = \frac{100 \times 1120}{100 + 6 \times 2} \]
\[ = \frac{100 \times 1120}{100 + 12} \]
\[ = \frac{112000}{112} \]
\[ = 1000 \]

### Step 2: Calculate the Present Worth of B's Debt to A
B owes A Rs. 1081.50, which is payable in 6 months (0.5 years). We will use the same formula for present worth:

Where:
- Amount = Rs. 1081.50
- R = 6% per annum
- T = 0.5 years

Substituting the values:

\[ \text{Present Worth of B's Debt} = \frac{100 \times 1081.50}{100 + 6 \times 0.5} \]
\[ = \frac{100 \times 1081.50}{100 + 3} \]
\[ = \frac{108150}{103} \]
\[ \approx 1050 \]

### Step 3: Compare the Present Worths
Now we compare the present worth of both debts:
- Present Worth of A's Debt to B = Rs. 1000
- Present Worth of B's Debt to A = Rs. 1050

### Step 4: Determine Who Should Pay and How Much
Since B's present worth (Rs. 1050) is greater than A's present worth (Rs. 1000), B owes A the difference:

\[ \text{Amount B should pay to A} = \text{Present Worth of B's Debt} - \text{Present Worth of A's Debt} \]
\[ = 1050 - 1000 = 50 \]

### Conclusion
B should pay A Rs. 50 to settle their accounts.

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