Question

A sum of money borrowed on compound interest for 2 yrs at 20% and it would fetch 482RS more if the interest was payable half yearly than if were payable yearly,then the borrowed sum is?

Answer 1

Answer :

Given
Rate r = 20%
Time t = 2 years
Let sum of money = x
Then according to question , we get

x ${\left[1+\frac{20}{100}\right]}^2$ + 482 = x ${\left[1+\frac{{\displaystyle \frac{20}{2}}}{100}\right]}^{2\times 2}$

x ${\left[\frac{6}{5}\right]}^2$ + 482 = x${\left[\frac{11}{10}\right]}^4$

x$\frac{36}{25}$ + 482 = x$\left[\frac{14641}{10000}\right]$

x$\left[\frac{14641}{10000}\right]$ - x$\frac{36}{25}$ ​ =482

Taking L.C.M. we get

$\frac{14641x-14400x}{10000}=482$

241x = 4820000

x = 20000
So,
Sum of money = Rs. 20000 ( Ans )