If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

Question: If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

Solution:
Let the price be Tk. x per kg
Consumption be y kg

Expenditure = price × consumption
⇒ Expenditure = x × y

Price of sugar is increased by 10%
New price of sugar = Tk. 1.1x per 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% ≈ 9.1%