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%

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