Question

The difference in compound interest, and simple interest on a certain amount at 10% per annum at the end of the third year is RS. 620. What is the principal amount?

• A. 40000
• B. 12000
• C. 10000
• D. 20000

Answer 1

The correct option is D 20000

$\begin{array}{cc}& \text{Let the sum be Rs.}x\text{. Then,}\\ CI& =x{(1+\frac{10}{100})}^3-x\\ & =(\frac{1331}{1000}x-x)=\frac{331x}{1000}\\ S.I.& =\frac{x\times 10\times 3}{100}=\frac{3x}{10}\\ \therefore (C.I)-(S.I)& =(\frac{331x}{1000}-\frac{3x}{10})=\frac{31x}{1000}\\ \therefore \frac{31x}{1000}=620& \\ orx& =20000.\\ & \text{Hence, the principal amount is Rs. 20000.}\\ \text{Alternative:}& \\ (CI-SI{)}_{3}Y& =3P{\left(\frac{R}{100}\right)}^2+P{\left(\frac{R}{100}\right)}^3.\end{array}$