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(B) Let the sum be $P = Rs. 100$.Time $(T) = 2$ years.Rate $(R) = 15 \%$ per annum.Simple Interest $(S.I.) = \frac{P 	imes R 	imes T}{100} = \frac{1

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$650$

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(B) Let the sum be $P = Rs. 100$.Time $(T) = 2$ years.Rate $(R) = 15 \%$ per annum.Simple Interest $(S.I.) = \frac{P 	imes R 	imes T}{100} = \frac{100 	imes 15 	imes 2}{100} = Rs. 30$.True Discount $(T.D.) = \frac{P 	imes R 	imes T}{100 + (R 	imes T)} = \frac{100 	imes 15 	imes 2}{100 + (15 	imes 2)} = \frac{3000}{130} = Rs. \frac{300}{13}$.The difference between $S.I.$ and $T.D.$ is $S.I. - T.D. = 30 - \frac{300}{13} = \frac{390 - 300}{13} = Rs. \frac{90}{13}$.If the difference is $Rs. \frac{90}{13}$,the sum is $Rs. 100$.If the difference is $Rs. 45$,the sum is $100 	imes \frac{13}{90} 	imes 45 = 100 	imes \frac{13}{2} = Rs. 650$.

The difference between the simple interest and the true discount on a certain sum of money for $2$ years at $15 \%$ per annum at simple interest is $Rs. 45$. Find the sum (in $Rs.$).

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