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(B) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For the first period $t$,the ratio of principal to amount is $P : (P + SI_t)

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$5$

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(B) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For the first period $t$,the ratio of principal to amount is $P : (P + SI_t) = 4 : 5$.This implies $P + SI_t = \frac{5}{4}P$,so $SI_t = \frac{1}{4}P$.Using $SI = \frac{P 	imes R 	imes t}{100}$,we have $\frac{P 	imes R 	imes t}{100} = \frac{1}{4}P$,which gives $Rt = 25$.After $3$ years,the time becomes $t + 3$. The ratio of principal to amount is $P : (P + SI_{t+3}) = 5 : 7$.This implies $P + SI_{t+3} = \frac{7}{5}P$,so $SI_{t+3} = \frac{2}{5}P$.Using the formula again,$\frac{P 	imes R 	imes (t+3)}{100} = \frac{2}{5}P$,which gives $R(t+3) = 40$.Expanding this,$Rt + 3R = 40$.Substituting $Rt = 25$,we get $25 + 3R = 40$.$3R = 15$,so $R = 5$.The rate of interest is $5 \%$ per annum.

With a given rate of simple interest,the ratio of principal and amount for a certain period of time is $4:5$. After $3$ years,with the same rate of interest,the ratio of the principal and amount becomes $5:7$. The rate of interest per annum is (in $\%$):

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