There is 40% increase in an amount in 10 years at simple interest. What will be the compound interest of Rs. 30000 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 = $$\frac{P \times R \times T}{100}$$

=> $$40x = \frac{100x \times 10 \times R}{100}$$

=> $$R = \frac{40}{10} = 4\%$$

Compound interest of Rs. 30,000 for 3 years = $$P [(1 + \frac{R}{100})^T - 1]$$

= $$30,000 [(1 + \frac{4}{100})^3 - 1]$$

= $$30,000 [(\frac{26}{25})^3 - 1]$$

= $$30,000 \times \frac{17576 - 15625}{(25)^3} = 48 \times \frac{1951}{25}$$

= $$\frac{93648}{25} = Rs$$ $$3745.92$$

=> Ans - (A)