Question
The compound interest accrued on an amount of Rs. 25500 at the end of 3 years is Rs. 8440.50. What would be the simple interest accrued on the same amount at the same rate in the same period ?
Answer: Option D
$$\eqalign{
& {\text{Let the rate be R}}\% {\text{ p}}{\text{.a}}{\text{. }} \cr
& {\text{then,}} \cr
& {\text{25500}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} \cr
& = 25500 + 8440.50 \cr
& = 33940.50 \cr} $$
$$ \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} = \frac{{33940.50}}{{25500}} = $$ $$\frac{{1331}}{{1000}} = $$ $${\left( {\frac{{11}}{{10}}} \right)^3}$$
$$\eqalign{
& \Rightarrow 1 + \frac{{\text{R}}}{{100}} = \frac{{11}}{{10}} \cr
& \Rightarrow \frac{{\text{R}}}{{100}} = \frac{1}{{10}} \cr
& \Rightarrow {\text{R}} = 10\,\% \cr
& S.I. = {\text{R}}s.\left( {\frac{{25500 \times 10 \times 3}}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,7650 \cr} $$
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$$\eqalign{
& {\text{Let the rate be R}}\% {\text{ p}}{\text{.a}}{\text{. }} \cr
& {\text{then,}} \cr
& {\text{25500}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} \cr
& = 25500 + 8440.50 \cr
& = 33940.50 \cr} $$
$$ \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} = \frac{{33940.50}}{{25500}} = $$ $$\frac{{1331}}{{1000}} = $$ $${\left( {\frac{{11}}{{10}}} \right)^3}$$
$$\eqalign{
& \Rightarrow 1 + \frac{{\text{R}}}{{100}} = \frac{{11}}{{10}} \cr
& \Rightarrow \frac{{\text{R}}}{{100}} = \frac{1}{{10}} \cr
& \Rightarrow {\text{R}} = 10\,\% \cr
& S.I. = {\text{R}}s.\left( {\frac{{25500 \times 10 \times 3}}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,7650 \cr} $$
Was this answer helpful ?
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