Rs.3.903 is divided between A and B. so that A‘s share at the end of 7 years will be equal to B's share at the end of 9 years. with interest being compounded annually at the rate of 4% per annum. The share of A is:

Correct option is C

​Given:

Total amount = Rs. 3,903.

Interest is compounded annually at 4% per annum.

A's share after 7 years = B's share after 9 years.

Formula Used:

Compound Interest formula:

​$$A = P \left(1 + \frac{r}{100}\right)^t$$​​

Solution:

Let A's present share be x.

Then, B's present share = $$3903 - x$$​

Equate the future values: $$x \left(1 + \frac{4}{100}\right)^7 = (3903 - x) \left(1 + \frac{4}{100}\right)^9$$​

​$$x (1.04)^7 = (3903 - x)(1.04)^9$$​​

​$$x = (3903 - x)(1.04)^2$$​​

​$$x = (3903 - x)(1.0816)$$​​

​$$x = 3903 \times 1.0816 - x \times 1.0816$$​​

x=3903×1.0816−x×1.0816

$$x + x \times 1.0816 = 3903 \times 1.0816$$​

$x(1+1.0816)=3903\times 1.0816$

$$x \times 2.0816 = 4221.3648$$​

$$x=\frac{4221.3648}{2.0816}≈2,028$$​