There is 40% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 25000 after 3 years at the same rate?

Let the principal = $$Rs. 100x$$

=> Amount after simple interest = $$\frac{140}{100} \times 100 = Rs. 140x$$

=> Simple interest = $$140x - 100x = Rs. 40x$$

Simple interest = $$\frac{P \times R \times T}{100}$$

=> $$40x = \frac{100x \times 5 \times R}{100}$$

=> $$R = \frac{40}{5} = 8\%$$

Compound interest of Rs. 25,000 for 3 years = $$P [(1 + \frac{R}{100})^T - 1]$$

= $$25,000 [(1 + \frac{8}{100})^3 - 1]$$

= $$25,000 [(\frac{27}{25})^3 - 1]$$

= $$25,000 \times \frac{19683 - 15625}{(25)^3} = 4058 \times \frac{8}{5}$$

= $$4058 \times 1.6 = Rs$$ $$6492.8$$

=> Ans - (A)