Compound Interest — Divide ₹ 2,602 between M and N so that M’s amount after 7 years equals N’s amount after 9 years at 4% per annum compounded annually. Find individual shares.

Introduction / Context:
We split a fixed principal between two people so that their future amounts (at different times) are equal under the same compound-interest rate.

Given Data / Assumptions:

• Total = ₹ 2,602.
• Rate = 4% p.a. compounded annually.
• M grows for 7 years; N grows for 9 years.

Concept / Approach:
Let M's share be x ⇒ N's share = 2,602 − x. The equality of future amounts is x*(1.04)^7 = (2,602 − x)*(1.04)^9. Canceling the common factor (1.04)^7 gives x = (2,602 − x)*(1.04)^2.

Step-by-Step Solution:
(1.04)^2 = 1.0816x = 1.0816*(2,602 − x) ⇒ x + 1.0816x = 2,602*1.08162.0816x = 2,814.3232 ⇒ x = ₹ 1,352N's share = 2,602 − 1,352 = ₹ 1,250

Verification / Alternative check:
Check equality: 1,352*(1.04)^7 equals 1,250*(1.04)^9 (since multiplying M by (1.04)^2 matches N's longer term).

Why Other Options Are Wrong:
Only ₹ 1,352 and ₹ 1,250 exactly satisfy the compounding relation; other pairs do not.

Common Pitfalls:
Forgetting to cancel common powers or using simple interest instead of compound interest.

Final Answer:
₹ 1,352, ₹ 1,250