If at same rate of interest, in 2 years, the simple interest is Rs. 42 and compound interest is Rs. 45, then what is the principal (in Rs. )?

Correct option is A

Given:

Simple Interest (SI) for 2 years = Rs. 42

Compound Interest (CI) for 2 years = Rs. 45

Same rate of interest, same principal

Concept Used:

Simple Interest (SI) is uniform each year.

Compound Interest (CI) adds interest on interest.

Difference between CI and SI in 2 years gives extra interest = interest on 1st year’s interest.

Formula Used:

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

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

Solution:

SI for 2 years = 42 

SI for 1 year = 21

CI for 2 years = 45 

CI for 1st year = 21, CI for 2nd year = 24

Extra interest = 24 - 21 = 3 = interest on Rs. 21

R = $$\frac{3}{21} \times 100 = \frac{100}{7} \% \approx 14.28\%$$​​

From SI formula (1 year):

21 = $$\frac{P \times \tfrac{100}{7}}{100}$$​​

21 = $$\frac{P}{7}$$​​

P = 147 

Alternate Solution(Exam-hall Method):