If at same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is ₹65, then what is the principal (in ₹)?

Correct option is B

Given:

- Time = 2 years

- Simple Interest (SI) = ₹40

- Compound Interest (CI) = ₹65

Formula Used:

- Difference between CI and SI for 2 years = $$P × (\frac{R}{100})²$$​​

Solution:

Difference (CI - SI) = ₹65 − ₹40 = ₹25

Let the rate be R% and principal be P

\$$25 = P \times \left( \frac{R}{100} \right)^2 = P \times \frac{R^2}{10000} ...... (1)\\\ \\ 40 = \frac{P \times R \times 2}{100} \Rightarrow P \times R = 2000 .......(2) \\$$​​

Substitute 

​$$P \text{ from (2) into (1):} \\\ \\\frac{2000}{R} \times \frac{R^2}{10000} = 25 \\\ \\\Rightarrow \frac{2000R}{10000} = 25 \\\ \\\Rightarrow 2000R = 250000 \\\ \\\Rightarrow R = \frac{250000}{2000} = 125 \\$$​​

Now, substitute 

R = 125 into equation (2):
​$$P = \frac{2000}{125} = ₹16$$​​
Final Answer: ₹16