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?

9.10%

Let the price of sugar per kg be Rs 50 and sugar consumption be 10 kg with expenditure of 50*10=Rs 500

Increased price of sugar by 10%=50*110/100=Rs 55

Quantity of sugar consumption to keep expenditure on sugar remain same=500/55=9.091 grams

Reduction in quantity of sugar consumption = 10.000 – 9.091 = 0.909

Percentage must a family reduce its consumption, so that the family's expenditures do not increase= 0.909/10 * 100 = 9.09% or 9.10%

OR

Let us assume,

Price(P) - 10, Qty(Q) - 10, Expenditure(E) = P*Q = 100

Price increases by 10%

P = 11, Q = ?, E = 100

Q = \(\frac{100 }{ 11}\)

Qty = 9.09

Reduced qty = 10 - 9.09 = 0.91

Reduced percentage = 0.91/10 * 100 = 9.10%