Rs 1301 is divided between A and B so that the amount of A after 7 years is equal to the amount of B after 9 years, if interest is compounded annually at 4% per annum. What is B's share of the money?

Introduction:
This problem involves dividing a sum between two people so that the future values of their shares at different times become equal under compound interest. It checks your understanding of how amounts grow over time and how to translate equality of future amounts into an equation involving present shares.

Given Data / Assumptions:

• Total sum to be divided between A and B = Rs 1301.
• Rate of compound interest r = 4% per annum.
• A's amount is considered after 7 years, B's amount after 9 years.
• Interest is compounded annually.
• Amounts of A and B after their respective periods are equal.
• We must find B's share.

Concept / Approach:
Let A's present share be x and B's present share be 1301 − x. After 7 years A's amount is x * (1.04)^7. After 9 years B's amount is (1301 − x) * (1.04)^9. Since these future amounts are equal, we equate them and solve for x. From this, we can derive B's share as 1301 − x.

Step-by-Step Solution:
Let A's present share = x. Then B's present share = 1301 − x.A's amount after 7 years = x * (1.04)^7.B's amount after 9 years = (1301 − x) * (1.04)^9.Given: x * (1.04)^7 = (1301 − x) * (1.04)^9.Divide both sides by (1.04)^7 to simplify:x = (1301 − x) * (1.04)^2.(1.04)^2 = 1.0816, so x = 1.0816 * (1301 − x).x = 1406.0496 − 1.0816x.x + 1.0816x = 1406.0496, so 2.0816x ≈ 1406.05.x ≈ 1406.05 / 2.0816 ≈ 676.Therefore B's share ≈ 1301 − 676 = Rs 625.

Verification / Alternative Check:
Use approximate shares: A gets Rs 676, B gets Rs 625. A's future amount after 7 years ≈ 676 * (1.04)^7. B's future amount after 9 years ≈ 625 * (1.04)^9. Because (1.04)^9 = (1.04)^7 * (1.04)^2, equality of amounts is consistent with the equation solved above. Using accurate calculator values, the two future amounts match closely, confirming the shares.

Why Other Options Are Wrong:
Rs 626 and Rs 627: These are very close but do not satisfy the equality of future amounts exactly.Rs 286: Far too small; this would make A's share much larger and disturb the balance of future values.Rs 675: This would leave A with only Rs 626, reversing the roles and not matching the equality with the given rate and times.

Common Pitfalls:
Students sometimes attempt to divide the sum directly in proportion to the times instead of using compound factors, or they neglect that B's amount accumulates interest for a longer period. It is essential to carefully write the equality of future amounts using the correct compounding factors.

Final Answer:
B's present share of the money is Rs 625.