# The price of rice is increased by 6.25% and the consumption of the family is decreased by 10%. What is the percentage change in the expenditure of the

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The price of rice is increased by 6.25% and the consumption of the family is decreased by 10%. What is the percentage change in the expenditure of the family?
1. 4.75%
2. 4.375%
3. 4.5%
4. 4%

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Correct Answer - Option 2 : 4.375%

Given:

% increase in price = 6.25%

% decrease in consumption = 10%

Concept:

Since, the percentage change is asked in the question, consider the original price and original consumption of the family to be 100%, then proceed.

Formula used:

Price × Consumption = Expenditure

% change = [(Initial value - Final value)/Initial value] × 100

Calculation:

Let, the original consumption = 100y

Original price = 100x

% increase in price = [6(1/4)]% × 100x

= (25/400) × 100x

= 6.25x

∴ New price = 100x + 6.25x

= 106.25x

% decrease in consumption = 10% of 100y

= (10/100) × 100y

= 10y

∴ New consumption = 100y - 10y

= 90y

∴ Initial expenditure = Initial price × Initial consumption

= (100x) × (100y)

= 10000xy

Final expenditure = (106.25x) × (90y)

= 9562.5xy

∴ % change in expenditure = [(10000xy - 9562.5xy)/10000xy] × 100

= 437.5/100

= 4.375%