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Petrol prices are reduced by 20%. Find by how much percent a vehicle owner must increase his consumption of petrol so as not to decrease his expenditure of petrol.
- a)20%
- b)25%
- c)42%
- d)None
- e)All of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Petrol prices are reduced by 20%. Find by how much percent a vehicle o...
Given:
- Petrol prices are reduced by 20%.
- We need to find by how much percentage a vehicle owner must increase his consumption so that his expenditure does not decrease.
Step 1: Understanding the situation.
If the price of petrol has decreased by 20%, it is now 80% of what it was before. To keep the expenditure the same, the vehicle owner must increase his consumption so that the total expenditure remains constant.
Step 2: Formula to calculate the percentage increase in consumption:
The formula to calculate the percentage increase required is:
In this case, the reduction in price is 20%, or 0.20.
In this case, the reduction in price is 20%, or 0.20.
Step 3: Substituting the values into the formula:
The vehicle owner must increase his consumption by 25% to maintain the same expenditure on petrol.
The vehicle owner must increase his consumption by 25% to maintain the same expenditure on petrol.
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Petrol prices are reduced by 20%. Find by how much percent a vehicle o...
Solution:
Let's assume that initially, the cost of petrol is Rs. 100
After a 20% reduction, the cost of petrol becomes Rs. 80
To keep the cost of petrol constant, the vehicle owner needs to increase his consumption of petrol. Let's say the vehicle owner initially consumed x liters of petrol.
Now, the cost of petrol per liter = 100/x
After the reduction, the cost of petrol per liter = 80/x
To keep the cost constant, the vehicle owner needs to consume y liters of petrol, where
100/x = 80/y
y = (4/5)x
Therefore, the vehicle owner needs to increase his consumption of petrol by (1 - 4/5) = 1/5 or 20%
Hence, the correct option is (b) 25%.
Note: It is important to understand that the percentage increase in consumption of petrol is always greater than the percentage reduction in petrol prices to keep the expenditure constant. In this case, the percentage reduction in petrol prices is 20%, but the percentage increase in consumption of petrol required to keep the expenditure constant is 25%.
Let's assume that initially, the cost of petrol is Rs. 100
After a 20% reduction, the cost of petrol becomes Rs. 80
To keep the cost of petrol constant, the vehicle owner needs to increase his consumption of petrol. Let's say the vehicle owner initially consumed x liters of petrol.
Now, the cost of petrol per liter = 100/x
After the reduction, the cost of petrol per liter = 80/x
To keep the cost constant, the vehicle owner needs to consume y liters of petrol, where
100/x = 80/y
y = (4/5)x
Therefore, the vehicle owner needs to increase his consumption of petrol by (1 - 4/5) = 1/5 or 20%
Hence, the correct option is (b) 25%.
Note: It is important to understand that the percentage increase in consumption of petrol is always greater than the percentage reduction in petrol prices to keep the expenditure constant. In this case, the percentage reduction in petrol prices is 20%, but the percentage increase in consumption of petrol required to keep the expenditure constant is 25%.
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