If the price of tea is increased by $ 20\%$, then by what percentage must a householder reduce her consumption

Question

If the price of tea is increased by $ 20\%$, then by what percentage must a householder reduce her consumption of tea so as to leave her expenditure on tea unchanged?

Examoogle · Accepted Answer

The correct answer is Option D: $16 \frac{2}{3}\%$. Use the fraction conversion: 20% increase is a ratio of 1/5. To keep expenditure constant, the consumption must decrease by the ratio 1/(5+1) = 1/6, which is 16 2/3%.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the fraction conversion: 20% increase is a ratio of 1/5. To keep expenditure constant, the consumption must decrease by the ratio 1/(5+1) = 1/6, which is 16 2/3%.

Formula Used: $$	ext{Reduction Percentage} = \left( \frac{x}{100 + x} ight) 	imes 100$$

Given: Price of tea is increased by 20%, and the total expenditure is to be kept constant.

Steps: Establish the relationship: Since Expenditure = Price × Consumption and expenditure is constant, the ratio of Consumption is inverse to the ratio of Price.. Calculate the price ratio: Initial price is $100$, new price is $100 + 20 = 120$. The ratio of Price becomes $120:100 = 6:5$.. Determine consumption reduction: The consumption must change from $6$ units to $5$ units. The reduction required is $1$ unit out of $6$.. Convert to percentage: Multiply the fraction by 100 to get the percentage value.

Answer: D is correct because a 20% price increase requires a 16 2/3% reduction in consumption to keep expenditure constant.

Exam Tip: This concept is identical to the 'speed-time-distance' relationship where distance is constant, speed and time are inversely proportional.

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