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- Quantitative Aptitude
Mr. Dua invested money in two schemes $A$ and $B$ offering compound interest at $8 \%$ per annum and $9 \%$ per annum respectively. If the total amount of ineterest accrued through two schemes together in two years was ₹ $4818.30$ and the total amount invested was ₹ $27000$ . What was the amount (In ₹) invested in scheme $A$.
$12000$
$13500$
$15000$
Cannot be determined
Solution
Let the amount invested in scheme $A$ be $₹ x .$ $\therefore \quad$ Amount in shceme $B =(27000-x)$
$\therefore \quad$ C.I. for 2 years.
i.e.
$\begin{array}{l}=x\left[\left(1+\frac{8}{100}\right)^{2}-1\right]+(27000-x)\left[\left(1+\frac{9}{100}\right)^{2}-1\right]=4818.30 \\x\left[\left(\frac{27}{25}\right)^{2}-1\right]+(27000-x)\left[\left(\frac{109}{100}\right)^{2}-1\right]=4818.30\end{array}$
or $\quad \frac{x}{25^{2}}\left[(27)^{2}-(25)^{2}\right]+\frac{(27000-x)}{100^{2}}\left[(109)^{2}-(100)^{2}\right]=4818.30$
or $\frac{x}{25^{2}} \times 52 \times 2+\frac{27000-x}{10000} \times 209 \times 9=4818.30$
or $\frac{x}{100^{2}}\left[104 \times(4)^{2}-1881\right]=4818.30-1881 \times 2.7$
or
$\begin{array}{c}-\frac{217 x}{100^{2}}=-260.4 \\x=\frac{260.4 \times(100)^{2}}{217}=₹ 12000\end{array}$
