Question

The difference between ci and si on amount of rs15000 for 2years is rs 96. what is the rate of interest p.a.

Answer 1

$\mathbf{ \underline{ solution} : - }$




$\bold{ Given, }$

Principal ( P )= ₹ 15000
Difference between CI and SI = ₹ 96
Time ( T ) = 2 years
Rate ( R ) = ?





$\textbf{ \underline{Let the rate be x \% , }}$


Difference between CI and SI = ₹ 96

C.I. – S.I. = 96




$= > P \large{ \: [( \: } \small{1 + \frac{r}{100} }\large{)}^{n} - 1 \large{ ]} - \small{\frac{ P \times R \times T}{ 100 } } = 96$ $\\ \\ \\ \\ \\ = > 15000 \large{ [(} \small{1+ \frac{r}{100} } \large{)} ^{2} - \small{1}] - \small{\frac{15000 \times r \times 2}{100} } = 96$ $\\ \\ \\ \\ = > \small{ 15000}\large{[ } \small{\: \: ( \cancel{1} + \frac{r}{100} - \cancel{1})(1 + \frac{r}{100} + 1)} \large{]} - \small{ \frac{15000 \times 2r}{100} } = 96$ $\\ \\ \\ \\ = > \small{ 15000} \large{[(} \small{\frac{r}{100}} \large{)( } \small{\frac{r}{100} + 2} \large{)]} - \small{\frac{15000 \times 2 \times r}{100} } = 96$ $\\ \\ \\ \\ = > \small{ 15000} \large{[( }\small{\frac{r}{100} } \large{) } ^{2} \small{ + \frac{2r}{100} } \large{] } - [\small{ 15000 \times \frac{ 2r}{ 100}} ] = 96$ $\\ \\ \\ \\ = > \small{15000} \large{[ ( }\small{\frac{r}{100} + \cancel{ \frac{2r}{100}} - \cancel{ \frac{2r}{100} }} \large{)]} ^{2} = \small{96}$ $\\ \\ \\ \\ = > \small{15000} \large{(} \small{ { \frac{r}{100}} \large{ )}}^{2} = 96 \\ \\ \\ \\ = > 15000 \times \frac{r^{2} }{100 \times 100}$ $\\ \\ \\ \\ = > \frac{3}{2} \times {r}^{2} = 96 \\ \\ \\ \\ = > {r}^{2} = \frac{ \cancel{96} \: \: ^{32} \times 2}{ \cancel{3}} \\ \\ \\ \\ = > {r}^{2} = 32 \times 2 \\ \\ \\ \\ = > {r}^{2} = 64 \\ \\ \\ \\ = > r = \pm \: \sqrt{64} \\ \\ \\ \\ = > r = \pm \: 8$





Rate can't be negative, so rate will be the positive one that is 8.



Hence,
$\boxed{ \textcolor{aqua}{\bold{ \underline{ rate \: of \: the \: interest \: is \: \: 8 \% }}}}$