Target-Equality under CI — Split ₹ 3903 so that A after 7 years equals B after 9 years (4% p.a.): Divide ₹ 3903 between A and B such that A's amount after 7 years at 4% compound equals B's amount after 9 years at the same rate. Find the two shares.

Introduction / Context:When two parts of a sum will be left to grow for different durations at the same compound rate, equalizing their future amounts defines a proportional split today. This is a typical present-value balancing problem under compound interest.

Given Data / Assumptions:

• Total sum S = ₹ 3903
• Annual rate = 4% = 0.04
• A grows for 7 years; B grows for 9 years
• Condition: A's future amount = B's future amount

Concept / Approach:Let A's share be x; B's share is 3903 − x. Equality at maturity: x*(1.04)^7 = (3903 − x)*(1.04)^9. Divide both sides by (1.04)^7 to solve for x.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• All other splits do not satisfy x*(1.04)^7 = (3903 − x)*(1.04)^9.

Common Pitfalls:

• Forgetting to divide out common growth before solving; mixing SI and CI.

Final Answer:Rs. 2028 for A and Rs. 1875 for B.