Question

The compound interest on a certain sum for 2 years is rs. 105 and simple interest is rs. 100. find the rate of interest per annum and the sum.the compound interest on a certain sum for 2 years is rs. 105 and simple interest is rs. 100. find the rate of interest per annum and the sum.the compound interest on a certain sum for 2 years is rs. 105 and simple interest is rs. 100. find the rate of interest per annum and the sum.

Answer 1

$We \:have \: Compound \: Interest \:for \:2\\years (c.i) = Rs \: 105$

$and \: simple \: Interest \:for \:2\\years (c.i) = Rs \: 100$

$Let \: the \: sum ( Principal ) = Rs \: P$

$and \: rate \:of \: interest = R \% \: p.a$

$/blue { Difference \: between \: the \: s.i \: and}\\\blue{ c.i \: for \:2 \: years \: on \:the \: same}\\\blue { principal \:at \:same \: rate \:of \: Interest :}$

$\boxed { \pink { P\big(\frac{r}{100}\big)^{2} = c.i - s.i }}$

$\implies P\big(\frac{R}{100}\big)^{2} = 105 - 100$

$\implies P\big(\frac{R}{100}\big)^{2} = 5$

$\implies P = 5 \Big(\frac{100}{R}\Big)^{2} \: --(1)$

$Simple \: Interest \:for \:1 \:year = \frac{100}{2} \\= Rs \: 50$

$Time (T) = 1 \: year$

$Principal = P$

$R = \frac{ 100 \times s.i }{ P\times T }$

$\implies R= \frac{ 100\times 50}{ 5 \Big(\frac{100}{R}\Big)^{2} \times 1 } \: [ from \: (1) ]$

$\implies R = \frac{ 100 \times 50 \times R^{2}}{5 \times 100 \times 100 }$

$\implies R = \frac{R^{2}}{10}$

$\implies 10 = R$

$\implies R = 10\% \: --(2)$

/* Put value of R in equation (1) , we get */

$P = 5 \Big(\frac{100}{10}\Big)^{2}$

$\implies P = 5 \times 10^{2}$

$\implies P = Rs \:500$

Therefore.,

$\red { Sum } \green { = Rs \:500 }$

$\red { Rate \:of \: Interest } \green { = 10\% }$

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