   SEARCH HOME Math Central Quandaries & Queries  Question from Thanikasalam: It is understood that increase/decrease in profit for current year compared to the previous year is done by the formula (x-y)/y, with x=profit on current year and y=profit on previous year. How do we derive this formula? If we work on this formula of calculating increase/decrease in profit, we get x/y-1 * = (x-y)/y = x/y - y/y = x/y - 1 How do you justify the 1 in the equation above. How to derive the formula and how do i prove it? Thank You. Hi,

The expression $\large \frac{x - y}{y}$ expresses the increase in profit over last year $(x - y)$ as a fraction of last year's profit $y.$ You then manipulated this expression and showed that $\large \frac{x - y}{y} = \frac{x}{y} - 1$ and asked for the significance of the number 1.

Maybe it is more natural to think of this using percentages. For example if your profit last year was $y = \$20,000$and your profit this year was$\$25,000$ then $\large \frac{x - y}{y}$ yields $\frac14 = 0.25$ so your profit this year increased 25% over last year.

On the other hand $\large \frac{x}{y}$ yields $\frac54 = 1.25$ or said as a percentage that's 125%. Thus your profit this year is 125% of your profit last year. That's a 125% - 100% = 25% increase.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.