Question

A person borrows a certain amount of money at 5% simple interest and he lends that amount to another person at 10% compound interest, after three years his profit is Rs.905. Find out the amount he borrowed.

• A. Rs. 2000
• B. Rs. 3000
• C. Rs. 5000
• D. Rs. 8000

Answer 1

Answer: (C)

Rs. 5000

Given,
$\begin{array}{ccc}SI& ,& CI\\ r=5\left(percent\right)& ,& r=10\left(percent\right)\\ n=3& ,& n=3\\ SI=\frac{p\times n\times r}{100}& ,& CI=p{(1+\frac{10}{100})}^3-p\end{array}$
Also given, $CI.-SI=905$
$[p{(1+\frac{10}{100})}^3-p]-\frac{p\times 3\times 5}{100}=905$
$\therefore p[{\left(\frac{11}{10}\right)}^3-1]-\frac{3P}{20}=905$
$\therefore p[{\left(\frac{11}{10}\right)}^3-1-\frac{3}{20}]=905$
$\therefore p\left[\frac{1331-1150}{1000}\right]=905$
$\therefore p=\frac{905\times 1000}{181}$
$\therefore p=Rs.5000$