If the price of sugar is increased by 10%, then by how much percent consumption should be reduced so that the expenditure remains the same?

Let the price be Rs. x /kg

Consumption be y kg

Expenditure = price × consumption

⇒ Expenditure = x × y

Price of sugar is increased by 10%

New price of sugar = 1.1 x /kg

Let new consumption be z kg

New Expenditure = (1.1x) × z

New Expenditure = old Expenditure

⇒ (1.1x) × z = x × y

⇒ z = y/1.1

Reduction in consumption = (y - z) = y - y/1.1 = y/11

Percentage reduction in consumption=(reduction in consumption/original consumption)× 100

Percentage reduction in consumption = [(y/11)/y] × 100 = 100/11 = 9.09%

Shortcut method :

If the price of a commodity increases by r%, then the reduction in consumption so as not to increase the expenditure = [r/(100 + r)] × 100%

Percentage reduction in consumption = [10/(100 + 10)] × 100 = 1000/110 = 9.09%