We need to divide Total Sum Rs. 3364 between Ram and Sham so that Ram's share at the end of 5 years may equal to Sham's share at the end of seven years with compound interest rate at 5 percent.

Answer: Option B

Explanation:

It is clear from question that Ram's share after five years = Sham's share after seven years
Hence we can conclude following :

$$\begin{aligned} \text{(Rams's present share)}\left(1 + \dfrac{5}{100}\right)^5 = \text{(Sham's present share)}\left(1 + \dfrac{5}{100}\right)^7\\ => \dfrac{\text{(Ram's present share)}}{\text{(Sham's present share)}}= \dfrac{\left(1 + \dfrac{5}{100}\right)^7}{\left(1 + \dfrac{5}{100}\right)^5} \\ = \left(1 + \dfrac{5}{100}\right)^{(7-5)} = \left(1 + \dfrac{5}{100}\right)^2 \\ = \left(\dfrac{21}{20}\right)^2 = \dfrac{441}{400} \end{aligned}$$
Ram's present share : B's present share = 441 : 400

$$\begin{aligned} \text{As amount is Rs.3364, Ram's share = }3364 \times \dfrac{441}{(441+400)} \\\\ = 3364 \times \dfrac{441}{841} = 4 \times 441 = \text{ Rs. 1764} \end{aligned}$$

So Sham's share is = 3364-1764 = 1600