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(B) Let the principal be $P$,the rate of interest be $R$ per annum,and the time be $T = 2$ years.Simple Interest $(SI)$ for $2$ years = $P 	imes R

Vedclass · Accepted Answer

$500$

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(B) Let the principal be $P$,the rate of interest be $R$ per annum,and the time be $T = 2$ years.Simple Interest $(SI)$ for $2$ years = $P 	imes R 	imes 2 / 100 = 100$.Thus,$P 	imes R = 5000$.Compound Interest $(CI)$ for $2$ years = $P[(1 + R/100)^2 - 1] = 105$.$P[1 + R^2/10000 + 2R/100 - 1] = 105$.$P[R^2/10000 + 2R/100] = 105$.Since $P 	imes R = 5000$,we have $P 	imes R / 100 = 50$.Substituting $P 	imes R = 5000$ into the equation: $(5000 	imes R) / 10000 + (2 	imes 5000) / 100 = 105$.$0.5R + 100 = 105$.$0.5R = 5 \Rightarrow R = 10\%$.Now,using $P 	imes R = 5000$,we get $P 	imes 10 = 5000$.Therefore,$P = ₹ 500$.

If the compound interest on a certain sum for $2$ years is ₹ $105$ and simple interest is ₹ $100$,then the sum (in ₹) is:

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