Math

QuestionIf sugar prices rise by 25%25\%, by how much must a lady reduce her consumption to keep spending the same? (a) 25%25\% (b) 20%20\% (c) 30%30\% (d) None of these

Studdy Solution

STEP 1

Assumptions1. The price of sugar has increased by25% . The lady wants to keep her expenditure constant, i.e., she doesn't want to spend more money on sugar than she did before the price increase3. We need to find the percentage by which she needs to reduce her consumption to achieve this

STEP 2

Let's denote the original price of sugar as and the original quantity of sugar the lady buys as $Q$. Her original expenditure on sugar is then given byExpenditure_{original} = \\times Q$$

STEP 3

The price of sugar has increased by25%. This means the new price is +25%of +25\% \,of\,.

STEP 4

Convert the percentage to a decimal value.
25%=0.2525\% =0.25The new price of sugar is thennew=+times0.25=times1.25_{new} = + \\times0.25 = \\times1.25

STEP 5

Let's denote the new quantity of sugar the lady buys as QnewQ_{new}. The lady wants her expenditure to remain the same, so her new expenditure is also timesQ \\times Q. This gives us the equationExpenditureoriginal=ExpenditurenewExpenditure_{original} = Expenditure_{new}timesQ=newtimesQnew \\times Q =_{new} \\times Q_{new}

STEP 6

Substitute the new price new_{new} into the equation.
timesQ=(times1.25)timesQnew \\times Q = ( \\times1.25) \\times Q_{new}

STEP 7

olve the equation for QnewQ_{new}.
Qnew=timesQtimes1.25=Q1.25Q_{new} = \frac{ \\times Q}{ \\times1.25} = \frac{Q}{1.25}

STEP 8

The percentage reduction in quantity is then given byReductionpercentage=QQnewQtimes100%Reduction\, percentage = \frac{Q - Q_{new}}{Q} \\times100\%

STEP 9

Substitute QnewQ_{new} into the equation.
Reductionpercentage=QQ.25Qtimes100%Reduction\, percentage = \frac{Q - \frac{Q}{.25}}{Q} \\times100\%

STEP 10

implify the equation.
Reductionpercentage=(.25)times100%Reduction\, percentage = \left( - \frac{}{.25}\right) \\times100\%

STEP 11

Calculate the reduction percentage.
Reductionpercentage=20%Reduction\, percentage =20\%So, the lady needs to reduce her consumption by20% to keep her expenditure constant. The correct answer is (b) 20%20 \%.

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