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- Standard 13
- Quantitative Aptitude
A man borrows money at $3 \%$ per annum interest payable yearly and lend it immediately at $5 \%$ interest (compound) payable half-yearly and thereby gains ₹ $330$ at the end of the year. The sum borrowed (In ₹) is
$17000$
$16500$
$15000$
$16000$
Solution
(d) Let the amount borrowed be $₹ x$
$\therefore \quad$ Interest to be paid $=₹ \frac{x \times 3}{100}=₹ \frac{3 x}{100}$
$NoW$
Rate $=\frac{5}{2} \%$ per half-year Time $=2$ half-years $\therefore \quad CI =P\left[\left(1+\frac{R}{100}\right)^{T}-1\right]$
$=x\left[\left(1+\frac{5}{200}\right)^{2}-1\right]=x\left[\left(1+\frac{1}{40}\right)^{2}-1\right]$
$=x\left[\left(\frac{41}{40}\right)^{2}-1\right]=x\left[\left(\frac{1681}{1600}-1\right)\right]$
$=x\left(\frac{1681-1600}{1600}\right)=₹ \frac{81 x}{1600}$
Difference $=\frac{81 x}{1600}-\frac{3 x}{100}$
$=\frac{81 x-48 x}{1600}=₹ \frac{33 x}{1600}$
$\therefore \frac{33 x}{1600}=330$
$\Rightarrow \quad x=\frac{1600 \times 330}{33}=₹ 16000$
