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QuestionIf ghee's price rises by 30%30\%, what percent must a housewife reduce her consumption to maintain her spending?

Studdy Solution

STEP 1

Assumptions1. The price of ghee is increased by30% . The housewife wants to keep her expenditure constant3. The reduction in consumption is calculated as a percentage

STEP 2

Let's denote the original price of ghee as $$ and the original quantity consumed as $Q$. The total expenditure can be calculated as the product of the price and the quantity.
Expenditure=×QExpenditure = \times Q

STEP 3

The price of ghee is increased by30%. Let's denote the new price as ′'. We can calculate it as follows′=+0.3=1.3' = +0.3 =1.3

STEP 4

The housewife wants to keep her expenditure constant. Therefore, the new expenditure with the increased price and the reduced quantity (denoted as Q′Q') is still equal to the original expenditure.
′×Q′=×Q' \times Q' = \times Q

STEP 5

Substitute ′' from step3 into the equation from step4.
1.3×Q′=×Q1.3 \times Q' = \times Q

STEP 6

implify the equation by dividing both sides by $$.
1.3Q′=Q1.3Q' = Q

STEP 7

olve the equation for Q′Q'.
Q′=Q1.3Q' = \frac{Q}{1.3}

STEP 8

The reduction in consumption is the difference between the original quantity QQ and the new quantity Q′Q', divided by the original quantity QQ, and multiplied by100% to convert it to a percentage.
Reduction in consumption=(Q−Q′Q)×100%Reduction\, in\, consumption = \left(\frac{Q - Q'}{Q}\right) \times100\%

STEP 9

Substitute Q′Q' from step7 into the equation from step8.
Reduction in consumption=(Q−Q.3Q)×100%Reduction\, in\, consumption = \left(\frac{Q - \frac{Q}{.3}}{Q}\right) \times100\%

STEP 10

implify the equation.
Reduction in consumption=(−.3)×100%Reduction\, in\, consumption = \left( - \frac{}{.3}\right) \times100\%

STEP 11

Calculate the reduction in consumption.
Reduction in consumption=(−.3)×100%≈2313%Reduction\, in\, consumption = \left( - \frac{}{.3}\right) \times100\% \approx23 \frac{}{13} \%So, the housewife must reduce her consumption of ghee by approximately 2313%23 \frac{}{13} \% to keep her expenditure constant. Therefore, the correct answer is (b) 2313%23 \frac{}{13} \%.

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