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If the price of a commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?
- a)1/4
- b)1/3
- c)1/2
- d)2/3
Correct answer is option 'B'. Can you explain this answer?
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If the price of a commodity is increased by 50% by what fraction must ...
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{R = increase/decrease in 1st Quantity)
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If the price of a commodity is increased by 50% by what fraction must ...
To understand why the correct answer is option 'B', let's break down the problem step by step.
Let's assume the initial price of the commodity is 100 units. When the price is increased by 50%, the new price becomes 150 units.
Now, we need to find the fraction by which the consumption of the commodity must be reduced to maintain the same expenditure.
Let's consider the initial consumption of the commodity to be 'x' units. The initial expenditure would be the price multiplied by the consumption, which is 100 units * x units = 100x units.
After the price increase, the consumption needs to be reduced so that the expenditure remains the same. Let's call the reduced consumption 'y' units.
The new expenditure would be the new price multiplied by the reduced consumption, which is 150 units * y units = 150y units.
Since the expenditure needs to remain the same, we have the equation:
100x units = 150y units
Now, let's solve for y in terms of x:
150y units = 100x units
Dividing both sides of the equation by 150 units:
y = (100x units) / (150 units)
Simplifying the fraction:
y = (2x units) / (3 units)
From the equation, we can see that the reduced consumption 'y' is equal to (2x units) / (3 units).
Comparing this with the given options, we can see that the correct fraction is 2/3, which is option 'B'.
Let's assume the initial price of the commodity is 100 units. When the price is increased by 50%, the new price becomes 150 units.
Now, we need to find the fraction by which the consumption of the commodity must be reduced to maintain the same expenditure.
Let's consider the initial consumption of the commodity to be 'x' units. The initial expenditure would be the price multiplied by the consumption, which is 100 units * x units = 100x units.
After the price increase, the consumption needs to be reduced so that the expenditure remains the same. Let's call the reduced consumption 'y' units.
The new expenditure would be the new price multiplied by the reduced consumption, which is 150 units * y units = 150y units.
Since the expenditure needs to remain the same, we have the equation:
100x units = 150y units
Now, let's solve for y in terms of x:
150y units = 100x units
Dividing both sides of the equation by 150 units:
y = (100x units) / (150 units)
Simplifying the fraction:
y = (2x units) / (3 units)
From the equation, we can see that the reduced consumption 'y' is equal to (2x units) / (3 units).
Comparing this with the given options, we can see that the correct fraction is 2/3, which is option 'B'.
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If the price of a commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?a)1/4b)1/3c)1/2d)2/3Correct answer is option 'B'. Can you explain this answer?
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