profits increase between 1991 and 1993

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"What was the percent increase in profits for Company X between 1991 and 1993?"

does this question mean that we need to calculate the 1992 profit increase as well? I am unable to comprehend what does this question exactly mean.

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You don't need to, all you need to know is the profit in 1991 (call this $x_{1991}$) and in 1993 (call this $x_{1993}$). If you know these values, the percentage change in the profit from 1991 to 1993 is given by $$ \frac{x_{1993}-x_{1991}}{x_{1991}}\times 100\%.$$