If at same rate of interest, in 2 years, the simple interest is Rs. 40 and compound interest is Rs. 80, then what is the principal (in Rs. )?

Correct option is B

Given:

Time (T) = 2 years

Simple Interest (SI) = Rs. 40

Compound Interest (CI) = Rs. 80

We are to find the principal (P).

Formula Used:

The difference between Compound Interest and Simple Interest for 2 years is given by the formula:

Difference = P$$\left(\frac{R}{100}\right)^2$$​​

Solution:

Difference = CI – SI = 80 – 40 = 40

For the first year, SI = CI.

Since total SI for 2 years is Rs. 40, the SI for 1 year is Rs. 20. Therefore,

SI for 1 year = $$\frac{P \times R}{100}$$​ = 20 …..(1)

Now substituting the difference into the formula:

40 = $$P \left(\frac{R^2}{10000}\right)$$​​

So,

40 = $$\left(\frac{P \times R}{100}\right) \times \left(\frac{R}{100}\right)$$​​

From equation 1:

40 = $$20 \times \left(\frac{R}{100}\right)$$​​

1 = $$\frac{R}{100}$$​​

R = 200%

From simple interest formula;

40 = $$\frac{P \times 200 \times 2}{100}$$​​

40 = 4P

P = 10

Thus, the principal amount is Rs. 10