When difference between compound and simple interest for three years is Rs. 217 at 10% interest per annum, the principal is Rs. ______

Correct option is D

Given:

Difference (CI – SI) for 3 years = Rs 217

Rate = 10% p.a.

Formula Used: 

Difference of CI - SI for three year

CI – SI (3 yr)} = $$3P\left(\frac{r}{100}\right)^2 + P \left(\frac{r}{100}\right)^3$$​​

=$$P \times \left(\frac{r}{100}\right)^2 \times \left(3 + \frac{r}{100}\right)$$​​

​Solution: 

Applying the formula; 

​$$217 = P\times \left(\frac{10}{100}\right)^2 \times \left(3 + \frac{10}{100}\right)\\ \ \\217 = P \times (0.10)^2 \times (3 + 0.10) \\ \ \\217 = P \times (0.01) \times (3.1)\\ \ \\217 = 0.031P \\ \ \\P = \frac{217}{0.031} = 7000$$​​

Thus, the principal is Rs 7000. 

Exam hall Method: ​