If the ratio of C.I. and S.I. interest for th | vedclass

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(D) For $2$ years,the Compound Interest $(C.I.)$ is given by $C.I. = P \left[ \left( 1 + \frac{R}{100} \right)^2 - 1 \right] = P \left[ \frac{2R}{100}

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$40$

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(D) For $2$ years,the Compound Interest $(C.I.)$ is given by $C.I. = P \left[ \left( 1 + \frac{R}{100} ight)^2 - 1 ight] = P \left[ \frac{2R}{100} + \frac{R^2}{10000} ight]$.The Simple Interest $(S.I.)$ for $2$ years is $S.I. = \frac{P 	imes R 	imes 2}{100} = \frac{2PR}{100}$.The ratio is given as $\frac{C.I.}{S.I.} = 1.2$.Substituting the expressions: $\frac{P \left( \frac{2R}{100} + \frac{R^2}{10000} ight)}{\frac{2PR}{100}} = 1.2$.Simplifying the expression: $\frac{\frac{2R}{100} (1 + \frac{R}{200})}{\frac{2R}{100}} = 1 + \frac{R}{200} = 1.2$.Therefore,$\frac{R}{200} = 0.2$,which gives $R = 0.2 	imes 200 = 40 \%.$

If the ratio of $C.I.$ and $S.I.$ interest for the same principal and rate of interest for $2$ years is $1.2,$ find the rate of interest (in $\%$).

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