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%