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(A) The formula for the difference between $C.I.$ and $S.I.$ for $2$ years is given by: $Difference = P 	imes (R/100)^2$.From statement $(I)$,we can

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Only $I$

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(A) The formula for the difference between $C.I.$ and $S.I.$ for $2$ years is given by: $Difference = P 	imes (R/100)^2$.From statement $(I)$,we can calculate the rate of interest $(R)$:$S.I. = (P 	imes R 	imes T) / 100$$120 = (1000 	imes R 	imes 2) / 100$$120 = 20R \implies R = 6\%$.From statement $(II)$,we are given the principal $(P = 2000)$.To find the principal amount when the difference is $18$,we need both the rate $(R)$ and the difference. Since statement $(I)$ provides the rate and statement $(II)$ provides the principal,we need to check if they are consistent or if both are required to solve for a missing variable. Actually,if we use the formula $18 = P 	imes (R/100)^2$,we have two variables ($P$ and $R$). Statement $(I)$ gives $R=6\%$. If we use this in the formula,we can find $P$. Thus,statement $(I)$ alone is sufficient. However,if the question asks to verify the principal,statement $(I)$ is sufficient. Given the options,$(I)$ alone is sufficient.

Which information given below is sufficient to know the principal amount if the difference between the $C.I.$ and $S.I.$ for $2$ years is $18$?
$(I)$ The rate is same at which an amount of $Rs. 1000$ becomes $1120$ in $2$ years under $S.I.$
$(II)$ The principal is $Rs. 2000$.

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Which information given below is sufficient to know the principal amount if the difference between the $C.I.$ and $S.I.$ for $2$ years is $18$?$(I)$ The rate is same at which an amount of $Rs. 1000$ becomes $1120$ in $2$ years under $S.I.$$(II)$ The principal is $Rs. 2000$.