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(A) Let the sum be $P$ and the rate be $R\%$. Simple Interest $(SI)$ for $3$ years $= 240$,so $SI$ for $1$ year $= 240 / 3 = 80$. $SI$ for $2$ years $

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$2400, 3 \frac{1}{3}$

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(A) Let the sum be $P$ and the rate be $R\%$. Simple Interest $(SI)$ for $3$ years $= 240$,so $SI$ for $1$ year $= 240 / 3 = 80$. $SI$ for $2$ years $= 80 	imes 2 = 160$. Banker's Discount $(BD)$ for $2$ years $= 150$. We know that for the same time,$SI$ is the interest on the True Discount $(TD)$,and $BD$ is the interest on the Sum $(P)$. Here,$BD = 150$ and $SI = 160$ for $2$ years. The relationship between $Sum$,$BD$,and $TD$ is $Sum = (BD 	imes TD) / (BD - TD)$. Since $SI$ for $2$ years is $160$,$TD = 160$. $Sum = (150 	imes 160) / (160 - 150) = 24000 / 10 = 2400$. Rate of interest $R = (SI 	imes 100) / (P 	imes T) = (240 	imes 100) / (2400 	imes 3) = 10 / 3 = 3 \frac{1}{3} \%$.

If the banker's discount on a certain sum in $2$ years at a certain rate is $Rs. 150$ and the simple interest on the same sum in $3$ years is $Rs. 240$,find the sum (in $Rs.$) and the rate of interest (in $\%$).

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