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The price of an article is increased by 16 (2/3)%. By what percentage the customer should reduce his consumption such the expenditure is increased by only 12%?
- a)5%
- b)6%
- c)7%
- d)4%
- e)Not Attempted
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The price of an article is increased by 16 (2/3)%. By what percentage ...
We know that
Product of price and consumption is equal to the expenditure
Let the original price of article be x units
According to the question,
Price is increased by 24%
New price of article = x + 16(2/3)% of x = 7x/6
Let the original consumption be y
Original expenditure = xy
Expenditure is increased by 12%
New expenditure = xy + (12/100) × xy = 28xy/25
New consumption = (New expenditure)/(New Price)
New consumption = (28xy/25)/(7x/6) = 24y/25
Decrease in consumption = (y) – (24y/25) = y/25
Required percentage = (y/25)/y × 100 = 4%
Most Upvoted Answer
The price of an article is increased by 16 (2/3)%. By what percentage ...
We know that
Product of price and consumption is equal to the expenditure
Let the original price of article be x units
According to the question,
Price is increased by 24%
New price of article = x + 16(2/3)% of x = 7x/6
Let the original consumption be y
Original expenditure = xy
Expenditure is increased by 12%
New expenditure = xy + (12/100) × xy = 28xy/25
New consumption = (New expenditure)/(New Price)
New consumption = (28xy/25)/(7x/6) = 24y/25
Decrease in consumption = (y) – (24y/25) = y/25
Required percentage = (y/25)/y × 100 = 4%
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Community Answer
The price of an article is increased by 16 (2/3)%. By what percentage ...
Calculation:
Step 1: Finding the initial increase in price
Let the initial price of the article be $100.
The price is increased by 16 (2/3)% which is equivalent to 50/3%.
Therefore, the new price = $100 + $100 * (50/3)/100 = $100 + $50/3 = $350/3 = $116.67.
Step 2: Finding the new price to maintain the expenditure increase at 12%
Let the customer reduce consumption by x%.
Since the price is reduced by x%, the new price will be $116.67 - $116.67 * x/100.
The customer will also consume (100 - x)% of the initial quantity.
According to the question,
$100 * (100 - x)/100 * ($116.67 - $116.67 * x/100) = $100 * 112/100.
Solving the above equation, we get x ≈ 4%.
Therefore, the customer should reduce consumption by 4% to maintain the expenditure increase at 12%.
Final Answer: Option D (4%)
Step 1: Finding the initial increase in price
Let the initial price of the article be $100.
The price is increased by 16 (2/3)% which is equivalent to 50/3%.
Therefore, the new price = $100 + $100 * (50/3)/100 = $100 + $50/3 = $350/3 = $116.67.
Step 2: Finding the new price to maintain the expenditure increase at 12%
Let the customer reduce consumption by x%.
Since the price is reduced by x%, the new price will be $116.67 - $116.67 * x/100.
The customer will also consume (100 - x)% of the initial quantity.
According to the question,
$100 * (100 - x)/100 * ($116.67 - $116.67 * x/100) = $100 * 112/100.
Solving the above equation, we get x ≈ 4%.
Therefore, the customer should reduce consumption by 4% to maintain the expenditure increase at 12%.
Final Answer: Option D (4%)
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Question Description
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