Math CentralQuandaries & 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.


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,

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