When difference between compound and simple interest for three years is Rs. 155 at 10% interest per annum, the principal is Rs. ______

Correct option is C

Given:
The difference between compound interest and simple interest = 155
Rate of interest = 10%
Formula Used:
​$$CI = \text{Amount} - P = P\left(1 + \frac{r}{100}\right)^n - P$$ 
$$SI = \frac{P \times r \times t}{100}$$​​
Solution:
According to question,
​$$P\left(1 + \frac{10}{100}\right)^3 - P - \frac{P \times 10 \times 3}{100} = 155\\\Rightarrow P\left(\frac{1331}{1000} - 1 - \frac{3}{10}\right) = 155\\\Rightarrow P = \frac{155000}{31} = 5000\\$$
 The sum is Rs.5000
Alternate Solution: 

Difference between CI and SI for 3 years = $$P × (\frac{R}{100})^2 × \frac{(300 + R)}{100}$$​​

Solution:

$$155= P × (\frac{10}{100})^2 × (\frac{310}{100}) \\\ \\155= P × \frac{100}{10000} × (\frac{310}{100}) \\\ \\P= \text{Rs. 5000}$$