Math CentralQuandaries & Queries


Question from bharat, a student:

if price of a commodity increases by x% the to keep the expenditure same
the decrease in consumption should be (x/(x+100))*100, why?


I think you have an error in your expression. Suppose the old price is p dollars per unit and your consumption is C units them the expenditure is

p × C dollars.

The price per units now increases by x% so the new price is p × (1 + x/100) dollars per unit. If your new consumption is N units then your expenditure is

p × (1 + x/100) × N dollars.

If the expenditure is unchanged then

p × C = p × (1 + x/100) × N = p × [(100 + x)/100] × N.


N = C × 100/(100 + x).


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