Cash versus credit offer with simple interest (true discount) Kailash wants to sell his television. He has two offers: (A) ₹ 10,000 in cash today, or (B) ₹ 6,440 to be paid after 8 months on credit, when money is worth 18% per annum (simple interest). Which option gives Kailash the higher present worth?

Introduction / Context:
This problem tests true-discount style comparison between a cash offer now and a credit payment later. The correct approach is to convert the future credit amount into its present worth using simple interest and then compare with the cash figure offered today.

Given Data / Assumptions:

• Cash offer today = ₹ 10,000.
• Credit offer = ₹ 6,440 after 8 months.
• Simple interest rate r = 18% per annum.
• Time to credit payment t = 8 months = 8/12 year.

Concept / Approach:
Present worth PW of a future sum S due after t years at simple interest r is PW = S / (1 + r * t). We then compare this PW with the cash offer to decide which is financially better for the seller (Kailash).

Step-by-Step Solution:
t = 8/12 = 2/3 year.r * t = 0.18 * (2/3) = 0.12.PW of ₹ 6,440 = 6,440 / (1 + 0.12) = 6,440 / 1.12 = ₹ 5,750.Compare: ₹ 10,000 (cash) versus ₹ 5,750 (present worth of credit).Clearly, cash ₹ 10,000 is higher and therefore better.

Verification / Alternative check:
If Kailash invested ₹ 5,750 at 18% for 8 months, it would amount to ₹ 5,750 * (1 + 0.12) = ₹ 6,440 (the credit figure). Hence ₹ 5,750 now is equivalent to ₹ 6,440 after 8 months; since ₹ 10,000 is far more, cash wins decisively.

Why Other Options Are Wrong:
₹ 6,440 at credit: its present worth is only ₹ 5,750, which is lower than ₹ 10,000.“Both are equivalent” or “Cannot be determined” are incorrect because the interest rate and time are given, enabling a clear computation.

Common Pitfalls:
Confusing amount with present worth or mistakenly adding interest instead of discounting. Always discount future sums to the present to compare fairly.

Final Answer:
₹ 10,000 in cash