Question: The price of onions increases by 25%, by what percent should a housewife reduces the consumption so that expenditure on onions can be same as before?
- 14.28
- 16.66
- 20
- 25
- 33.33
“The price of onions increases by 25%, by what percent should a housewife reduces the consumption so that expenditure on onions can be same as before?''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section tests the candidates’ intellect and analytical thinking capabilities to solve quantitative problems. The students must respond to the question by doing appropriate calculations on the basis of proper mathematical rules. The students must know basic knowledge of mathematical calculations to solve GMAT Problem Solving questions. The mathematical problems of the GMAT Quant topic in the problem-solving part is an essential part that needs to be solved by reasonable quantitative skills.
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:
- The price of onions raised by 25%.
Find out:
- the percentage at which the consumption of onions would be reduced so that the expenditure on onions remains the same as before.
Since we know that
Expenditure = Consumption * Price
Let the expenditure be E, consumption be C and Price be P
This implies
E = C * P
With a 25% increase in the price of onions, expenditure will be:
E = C * (1.25P)
While consumption needs to be reduced, let’s assume the new consumption is C1
Therefore, C * P = C1 * (1.25P)
Therefore, C1 = 0.8C
This signifies that a reduction of 20% in consumption is needed for onions to ensure that expenditure remains the same as before.
Correct Answer: C
Approach Solution 2:
The problem statement informs that:
Given:
- The price of onions raised by 25%.
Find out:
- the percentage at which the consumption of onions would be reduced so that the expenditure on onions remains the same as before.
Let’s assume the price before increasing is 100.
Increased price= 25% of 100 = 25/100 + 100 = 125
When the price is raised to 125, she needs to reduce it by 25
When the price is raised to 1, she needs to reduce it by 25/125
Therefore, the rate of decrease in consumption= 25/125* 100= 20
Hence, the percentage at which the consumption of onions would be reduced so that the expenditure on onions remains the same as before = 20%
Correct Answer: C
Approach Solution 3:
The problem statement informs that:
Given:
- The price of onions raised by 25%.
Find out:
- the percentage at which the consumption of onions would be reduced so that the expenditure on onions remains the same as before.
We can find the answer to this problem in a quicker and easier way.
As per the formula, decrease in consumption = [% Price increase/(100 + % Price Increase)]×100
Therefore, if the price of onion rises by 25%
therefore, decrease in consumption = [25/(100+25)] × 100 = [25/125]×100 = 20
Hence, the consumption of onion should be reduced by 20 % so that the expenditure remains the same.
Correct Answer: C
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