Summary:
On January 1, 2017, A owes B rupees 21,000. A accepts three bills to settle the debt with B. The first bill is for rupees 6,000 for 2 months, which A retains. The second bill is for rupees 7,000 for 3 months, which A retains. The third bill is for rupees 8,000 for 4 months, which A discounts with the bank for rupees 7,500.

Explanation:

Step 1: Calculate the Interest:
To calculate the interest for each bill, we use the formula:

Interest = Principal * Rate * Time

1. For the first bill:
Principal = 6,000 rupees
Rate = ?
Time = 2 months

To determine the rate, we rearrange the formula as:

Rate = Interest / (Principal * Time)

Assuming the rate is R1:

R1 = ? / (6,000 * 2)

2. For the second bill:
Principal = 7,000 rupees
Rate = ?
Time = 3 months

To determine the rate, we use the same formula as above:

Rate = Interest / (Principal * Time)

Assuming the rate is R2:

R2 = ? / (7,000 * 3)

3. For the third bill:
Principal = 8,000 rupees
Rate = ?
Time = 4 months

To determine the rate, we use the same formula as above:

Rate = Interest / (Principal * Time)

Assuming the rate is R3:

R3 = ? / (8,000 * 4)

Step 2: Calculate the Amount:
The amount to be settled for the third bill is given as 7,500 rupees. This amount is calculated using the formula:

Amount = Principal - Interest

Assuming the principal is P3:

P3 - (Interest calculated using R3) = 7,500 rupees

Step 3: Settling the Debt:
A retains the first bill and second bill, which means B and C will receive 6,000 rupees and 7,000 rupees respectively after the specified time period. For the third bill, A discounts it with the bank, meaning A receives 7,500 rupees immediately instead of waiting for the full amount at the end of 4 months.

Conclusion:
By accepting the three bills, A settles the debt with B. A retains the first and second bills, while discounting the third bill with the bank. This allows A to settle the debt in a staggered manner and also receive immediate payment for the discounted bill.