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₹ $6,100$ was partly invested in Scheme $A$ at $10 \%$ p.a. compound interest (compounded annually) for $2$ years and partly in Scheme $B$ at $10 \%$ p.a. simple interest for $4$ years. Both the schemes pay equal interests. How much was invested (In ₹) in Scheme $A$?
$3750$
$4500$
$4000$
$3250$
Solution
(c) Let amount invested in scheme $A=₹ x$
Let amount invested in scheme $B =₹(6100-x)$
$P_{1}\left[\left(1+\frac{R_{1}}{100}\right)^{T_{1}}-1\right]=\frac{P_{2} R_{2} T_{2}}{100}$
$x=\left[\left(1+\frac{10}{100}\right)^{2}-1\right]$
$x=\frac{(6100-x) \times 10 \times 4}{100}$
$\Rightarrow x \times\left[\left(\frac{11}{10}\right)^{2}-1\right]=4\left(\frac{6100-x}{10}\right)$
$x \times\left(\frac{121-100}{100}\right)=\frac{4(6100-x)}{10}$
$\Rightarrow \frac{21 x}{100}=\frac{24400-4 x}{10}$
$21 x=244000-40 x$
$21 x+40 x=244000$
$61 x=244000$
$x=₹ 4000$
