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MathematicsPercentage
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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?

A

15%

B

20%

C

25%

D

30%

Correct Answer

ЁЯУР MA тАв Math Direct FormulaMathematicsPercentage
Option B

20%

Quick Summary:

Use the fraction conversion: 25% is 1/41/41/4. Since price increases, the denominator becomes 1/(4+1)=1/51/(4+1) = 1/51/(4+1)=1/5. Multiply 1/51/51/5 by 100 to get 20%.

ЁЯУРMAMath SolutionDirect Formula
ЁЯУЛ Given

The price of a commodity increases by 25%. Expenditure is kept constant.

ЁЯФв Formula Used

Reduction%=(r100+r)├Ч100\text{Reduction} \% = \left( \frac{r}{100 + r} \right) \times 100Reduction%=(100+rrтАЛ)├Ч100

тЪб Exam Hall Shortcut / Speed Trick

Use the fraction conversion: 25% is 1/41/41/4. Since price increases, the denominator becomes 1/(4+1)=1/51/(4+1) = 1/51/(4+1)=1/5. Multiply 1/51/51/5 by 100 to get 20%.

тЪая╕П Common Student Trap / Pitfall

Students often mistakenly subtract 25% from 100% and answer 75%, or apply the percentage increase directly to the consumption instead of the denominator.

ЁЯУК Diagram / Illustration
Percentage Reduction in Consumption 1 Given Data Price Increase (r) = 25% | Expenditure = Constant 2 Formula Method Reduction % = [r / (100 + r)] ├Ч 100 = [25 / 125] ├Ч 100 3 Fractional Shortcut 25% = 1/4. New Consumption = 1/(4+1) = 1/5 = 20% 4 Final Result Required Reduction = 20% Correct Answer: 20% (Option B)
ЁЯФв Step-by-Step Solution
1

Define the variables

Let the initial price be 100 and initial consumption be 100. Expenditure is 100├Ч100=10000100 \times 100 = 10000100├Ч100=10000. After a 25% price increase, the new price is 125.

Pnew=125P_{new} = 125PnewтАЛ=125

2

Set up the expenditure equation

To keep expenditure constant at 10000, the new consumption CnewC_{new}CnewтАЛ must satisfy 125├ЧCnew=10000125 \times C_{new} = 10000125├ЧCnewтАЛ=10000.

Cnew=10000125=80C_{new} = \frac{10000}{125} = 80CnewтАЛ=12510000тАЛ=80

3

Calculate the percentage reduction

The reduction in consumption is 100тИТ80=20100 - 80 = 20100тИТ80=20. The percentage reduction is 20100├Ч100\frac{20}{100} \times 10010020тАЛ├Ч100.

Reduction=20%\text{Reduction} = 20\%Reduction=20%

тЬЕ

B is correct because a 25% increase in price requires a 20% reduction in consumption to maintain the same expenditure level.

Core Concepts Used
Click any tag to open in AI Tutor
Percentage Inverse Proportion Expenditure Stability Ratio-to-Percentage Conversion
ЁЯТб EXAM TIP

This concept is identical to the 'Speed-Time-Distance' problem where if speed increases, time taken decreases for the same distance: T=D/ST = D/ST=D/S.

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