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(B) Let the principal sum be $P$ and the rate of interest be $R \%$.Given: Simple Interest $(SI) = Rs. 100$,Compound Interest $(CI) = Rs. 110$,Time $(

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$Rs. 250$,rate $20 \%$ p.a.

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(B) Let the principal sum be $P$ and the rate of interest be $R \%$.Given: Simple Interest $(SI) = Rs. 100$,Compound Interest $(CI) = Rs. 110$,Time $(t) = 2$ years.For $2$ years,the formula for Simple Interest is $SI = \frac{P 	imes R 	imes t}{100} = \frac{P 	imes R 	imes 2}{100} = 100$,which implies $P 	imes R = 5000$.The difference between Compound Interest and Simple Interest for $2$ years is given by $CI - SI = \frac{P 	imes R^2}{100^2}$.Substituting the values: $110 - 100 = \frac{P 	imes R^2}{10000} \Rightarrow 10 = \frac{(P 	imes R) 	imes R}{10000}$.Since $P 	imes R = 5000$,we have $10 = \frac{5000 	imes R}{10000} \Rightarrow 10 = \frac{R}{2} \Rightarrow R = 20 \%$.Now,substitute $R = 20$ into $P 	imes R = 5000$: $P 	imes 20 = 5000 \Rightarrow P = 250$.Therefore,the sum is $Rs. 250$ and the rate of interest is $20 \%$ p.a.

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