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If the price of a commodity increases by 25%, by what percentage must a consumer reduce consumption so that the expenditure remains the same?
15%
20%
25%
30%
20%
Use the fraction conversion: 25% is 1/4. Since price increases, the denominator becomes 1/(4+1)=1/5. Multiply 1/5 by 100 to get 20%.
The price of a commodity increases by 25%. Expenditure is kept constant.
Reduction%=(100+rrтАЛ)├Ч100
Use the fraction conversion: 25% is 1/4. Since price increases, the denominator becomes 1/(4+1)=1/5. Multiply 1/5 by 100 to get 20%.
Students often mistakenly subtract 25% from 100% and answer 75%, or apply the percentage increase directly to the consumption instead of the denominator.
Define the variables
Let the initial price be 100 and initial consumption be 100. Expenditure is 100├Ч100=10000. After a 25% price increase, the new price is 125.
PnewтАЛ=125
Set up the expenditure equation
To keep expenditure constant at 10000, the new consumption CnewтАЛ must satisfy 125├ЧCnewтАЛ=10000.
CnewтАЛ=12510000тАЛ=80
Calculate the percentage reduction
The reduction in consumption is 100тИТ80=20. The percentage reduction is 10020тАЛ├Ч100.
Reduction=20%
B is correct because a 25% increase in price requires a 20% reduction in consumption to maintain the same expenditure level.
This concept is identical to the 'Speed-Time-Distance' problem where if speed increases, time taken decreases for the same distance: T=D/S.