Rice is now being sold at Rs. 40 a kg. During last month its rate was Rs. 32 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?
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25
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20
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40
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30
When price increases from Rs. 32 to Rs. 40, it's a 25% increase. To keep total expenditure constant, consumption must decrease by 20% because 0.80 × 40 = 32 (the original expenditure per kg). The formula for reduction percentage when price increases is: reduction% = increase%/(100+increase%) × 100 = 25/125 × 100 = 20%.
To solve this problem, we need to calculate the percentage reduction in consumption of rice.
Let's assume the initial consumption of rice by the family was x kg.
The initial expenditure on rice was (x kg * Rs. 32 per kg) = Rs. 32x.
Now, the current price of rice is Rs. 40 per kg. So, the new expenditure on rice would be (x kg * Rs. 40 per kg) = Rs. 40x.
To keep the expenditure fixed, the new expenditure should be equal to the initial expenditure.
Therefore, we have the equation:
Rs. 40x = Rs. 32x
Simplifying the equation, we get:
8x = 0
This means that the family should reduce its consumption of rice by 8x kg.
To find the percentage reduction, we can calculate:
Percentage reduction = (reduction in consumption / initial consumption) * 100
Percentage reduction = (8x / x) * 100 = 800%
Therefore, the family should reduce its consumption by 800%.
Now, let's go through the options:
Option A) 25 - This option is incorrect because the percentage reduction is 800%, not 25%. Option B) 20 - This option is correct because the percentage reduction is 800%, not 20%. Option C) 40 - This option is incorrect because the percentage reduction is 800%, not 40%. Option D) 30 - This option is incorrect because the percentage reduction is 800%, not 30%.
The correct answer is B) 20. This option is correct because the percentage reduction in consumption is 800%, which is equivalent to a 20% reduction.
I hope this explanation helps! Let me know if you have any further questions.