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| Math Central | Quandaries & Queries |
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Question from bharat, a student: if price of a commodity increases by x% the to keep the expenditure same |
Bharat,
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.
Thus
N = C × 100/(100 + x).
Penny
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