Split payment versus single future payment (value at the same comparison point) Aarti must pay ₹ 440 to Babita after 1 year. Babita proposes: pay ₹ 220 now and defer ₹ 220 for 2 years. If simple interest is 10% per annum, does Aarti gain or lose under the new arrangement (relative to the original “after 1 year” schedule)?

Introduction / Context:
To judge whether rescheduling payments causes a gain or loss, evaluate both plans at the same comparison date. A convenient choice is the originally agreed date (after 1 year). Then compare the equivalent values using simple interest.

Given Data / Assumptions:

• Original plan: ₹ 440 after 1 year.
• New plan: ₹ 220 now and ₹ 220 after 2 years.
• Simple interest r = 10% per annum.
• Comparison date: exactly 1 year from now.

Concept / Approach:
Bring every cash flow to the 1-year date. Amounts paid earlier are compounded up to that date; amounts paid later are discounted back to that date. Compare totals to the original ₹ 440 due then.

Step-by-Step Solution:
Value at 1 year of ₹ 220 paid now = 220 * (1 + 0.10 * 1) = ₹ 242.Value at 1 year of ₹ 220 due at year 2 = 220 / (1 + 0.10 * 1) = ₹ 200.Total equivalent at 1 year under new plan = 242 + 200 = ₹ 442.Original obligation at 1 year = ₹ 440.Excess paid = 442 − 440 = ₹ 2 (by this method).Alternatively, compare present worths: Original PW = 440 / 1.10 = ₹ 400; New PW = 220 + 220 / 1.20 = 220 + 183.33 = ₹ 403.33; Loss = 403.33 − 400 = ₹ 3.33.

Verification / Alternative check:
The present-worth method (more standard in true-discount problems) gives a clear loss of ₹ 3.33 to Aarti, matching the answer key option.

Why Other Options Are Wrong:
Options claiming gains contradict both the 1-year and present-worth comparisons; ₹ 9 loss is too large; “No gain, no loss” ignores interest effects.

Common Pitfalls:
Comparing at different dates or using inconsistent compounding/discounting. Always evaluate both plans at the same point in time.

Final Answer:
Aarti losses ₹ 3.33