Quandaries and Queries


what is the percentage difference between 157 to 251



When talking about percentages you should anways say "percentage OF WHAT". We quite often leave off the "of what" and that can cause confusion. For "percentage difference" I think of a quantity that has some value and then the value changes, and I ask "What is the difference, as a percentage of where you started?"

For your two numbers the difference is 251 - 157 = 94. If you were a storekeeper and bought an item for $157, marked it up $94 and sold it for $251 then I would say that your markup was $94. To express this as a percentage I would find 94 as a percent of 157, that is a percentage of where you started.

 94/157 100 = 59.9 %

and thus 157 increased 59.9% to 251.

If, on the other hand, you were a customer and saw an item in the window for sale that said "marked down from $251 to $157" you might wonder what is the percentage decrease. This time the value went from 251 to 157 and

 94/251 100 = 37.5 %

Thus 257 decreased 37.5% to 157.

94 is 59.9% of 157 and 94 is 37.5% of 251. Which percent you use depends on which way you are going. To be clear I wouldn't say "the difference between 157 and 251 is ??%" but rather "157 increased 59.9% to 251" or "251 decreased 37.5% to 157".



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