₹ 6,100 was partly invested in Scheme A at 10 % p.a. compound interest (compounded annually)

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6.Interest

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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

Let amount invested in scheme $B =₹(6100-x)$

$P_{1}\left[\left(1+\frac{R_{1}}{100}\right)^{T_{1}}-1\right]=\frac{P_{2} R_{2} T_{2}}{100}$

$x=\left[\left(1+\frac{10}{100}\right)^{2}-1\right]$

$x=\frac{(6100-x) \times 10 \times 4}{100}$

$\Rightarrow x \times\left[\left(\frac{11}{10}\right)^{2}-1\right]=4\left(\frac{6100-x}{10}\right)$

$x \times\left(\frac{121-100}{100}\right)=\frac{4(6100-x)}{10}$

$\Rightarrow \frac{21 x}{100}=\frac{24400-4 x}{10}$

$21 x=244000-40 x$

$21 x+40 x=244000$

$61 x=244000$

$x=₹ 4000$

Standard 13

Quantitative Aptitude

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easy

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medium

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medium

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medium

What sum of money (In ₹) at compound interest will amount to ₹ $650$ at the end of the first year and ₹ $676$ at the end of the second year?

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₹ 6,1006,100 was partly invested in Scheme AA at 10%10 \% p.a. compound interest (compounded annually) for 22 years and partly in Scheme BB at 10%10 \% p.a. simple interest for 44 years. Both the schemes pay equal interests. How much was invested (In ₹) in Scheme AA?

Solution

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