Formulae Percentage Commodity Increase and Expenditure
In this class, We discuss Formulae Percentage Commodity Increase and Expenditure.
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Formulae:
If the price of a commodity increase by R%, Then the reduction in consumption so as not to increase expenditure is
[(R/(100+R)) * 100]
If the price of a commodity decrease by R%, then the increase in consumption so as not to decrease the expenditure is
[(R/(100-R)) * 100]
Proof:
Let the price of commodity = x
Let consumption = y
Total expenditure = xy
If the price of a commodity increased by R%
New price = (x + (R/100)*x)
= x(R + (1/100))
New consumption = z
Expenditure same
x(R + (1/100))z = xy
z = y/(1+ R/100)
Percentage decrease in consumption = [ (y – (y/(1+ R/100))/y]*100
= y[(1 – (100/(100+R)))/y]*100
=(R/(100+R))*100%
Example:
The price of diesel increased by 25%. How much percent must a car owner reduce his consumption not to increase the expenditure?
Solution:
(R/(100+R)) * 100
= (25/(100+25)) * 100
= 20%