If at same rate of interest, in 2 years, the simple interest is Rs. 42 and compound interest is Rs. 43, then what is the principal (in Rs. )?

Correct option is A

Given:

Time (T) = 2 years

Simple Interest (SI) = ₹42

Compound Interest (CI) = ₹43

Difference (CI – SI) = ₹1

Concept Used:

For 2 years, the difference between Compound Interest and Simple Interest is:

CI - SI = Interest on 1st year's SI for 1 year at same rate

Formula Used:

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

Solution: ​

SI for 1 year = $$\frac{42}{2}$$​ = ₹21

Difference = $$\frac{21 \times R}{100}$$​ = 1

R = $$\frac{100}{21}\%$$​​

Now,

42 = $$\frac{P \times \frac{100}{21} \times 2}{100}$$​​

42 = $$\frac{2P}{21}$$​​

P = $$\frac{42 \times 21}{2}$$​ = ₹441