If at same rate of interest, in 2 years, the simple interest is Rs. 40 and compound interest is Rs. 50, then what is the principal (in Rs. )?

Correct option is A

Given:

Time = 2 years

Simple Interest (SI) = ₹40

Compound Interest (CI) = ₹50

Rate of interest is same for both SI and CI

We are to find the Principal (P)

Concept Used:

In 2 years, the difference between CI and SI is the interest on the first year’s SI, when compounded annually.

Simple interest is same every year.

Formula Used:

Simple Interest:

SI = $$\frac{P \times R \times T}{100}$$​​

Difference between CI and SI for 2 years:

CI - SI = $$\frac{P \times R^2}{100^2}$$​​

Also:

CI - SI = Interest on 1st year’s SI

Solution:

SI for 2 years = ₹40

SI for 1 year = ₹20

CI - SI = ₹50 - ₹40 = ₹10

This ₹10 is interest on ₹20 (1st year's SI) for 1 year:

​$$10 = \frac{20 \times R}{100} \Rightarrow R = 50$$​​

Using SI formula for 1 year:

​$$20 = \frac{P \times 50 \times 1}{100} \Rightarrow P = \frac{20 \times 100}{50} = ₹40$$​​