A price rises from 40 to 50, what percent gain?

Question

Percentage change trips people up on which number goes in the denominator. Solve in your head. What is the percentage increase from 40 to 50? Aim: under 8 seconds.

Accepted Answer

Percent change is the rise divided by the original value: \frac{50 - 40}{40} = \frac{10}{40} = \frac{1}{4} = 25\%. So the increase is \mathbf{25\%}. The base is the starting number 40, not the ending 50. Note the asymmetry: going back from 50 to 40 is a drop of 10/50 = 20\%. Up 25% and down 20% are inverses, not equal. Takeaway. Percent change = \dfrac{	ext{new} - 	ext{old}}{	ext{old}}. Always divide by the starting value; up-moves and down-moves between the same two prices are never equal percentages.

A price rises from 40 to 50, what percent gain?

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