If the price of Sugar decreases by 17%, what should be the approximate percentage increase in consumption of Sugar so as to keep the expenditure constant?

100 on 17% decrease comes to 83 and to keep expenditure constant we need to increase the percentage as (100-83)/83*100 =20.48%

17/(100-17)*100=20.48%

Let the Expenditure of the family be denoted by E.

Let the initial price of the sugar =P.

Let the initial consumption of sugar =C.

Expenditure(E)=Price∗Consumption=P∗C ————————-(1)

The price of the sugar is increased by 10%.

So the new price of sugar = P+10100P=P+0.1P=1.1P

Let the new Consumption = C’

The expenditure (E’) after a decrease in the sugar price, and, increase in the consumption = New Price * New Consumption=1.17P∗C′.——————-(2)

Expenditure before and after price increase should be the same.

Thus E = E’ and so, Equation 1 = Equation 2.

P∗C=1.17P∗C′

C=1.17C′

C’(New Consumption) = C1.17 ( Note: From this equation, it is evident that C’< C, and thus, with the decrease in Price, the consumption has increased to maintain the same Expenditure)

Percentage increase in consumption = (C−C′)C∗100

Percentage increase in consumption = (1.17C′−C′)1.17C′∗100

Percentage increase in consumption = 1.17C′∗100/0.83C'

Percentage increase in consumption = 20.48%.

Quick Shortcuts:

Shortcut 1: Percentage decrease in one variable (y) with percentage increase(P) in variable (x) = 100P/100-P

In the given question, variable x = Price of Sugar.

Percentage increase in variable x = P = 17

variable y = Consumption

Percentage increase in Consumption (y) = 100P/100-P=
100*17/100-17=1700/83=

Shortcut 2: Percentage increase in one variable (y) with percentage increase(P) in variable (x) = 100P/100-P

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