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When the price of rice is increased by 30 percent, a family reduces its consumption such that the expenditure is only 20 percent more than before. If 50 kg of rice is consumed by family before, then find the new consumption of family (approx.)
- a)43kg
- b)44kg
- c)45kg
- d)46kg
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
When the price of rice is increased by 30 percent, a family reduces it...
Suppose initially price per kg of rice is 100 then their expenditure is 5000.
Now their expenditure is only increased by only 20% i.e – 6000.
Increased price of rice = 130.
So new consumption = 6000/130 = 46
Now their expenditure is only increased by only 20% i.e – 6000.
Increased price of rice = 130.
So new consumption = 6000/130 = 46
Most Upvoted Answer
When the price of rice is increased by 30 percent, a family reduces it...
Problem Breakdown
To find the new consumption of rice by the family after a price increase, we will analyze the changes in expenditure and price.
Initial Information
- Initial Consumption: 50 kg of rice
- Price Increase: 30%
- Expenditure Increase: 20%
Calculating Initial Expenditure
1. Let the initial price of rice be P per kg.
2. Initial expenditure (E1) = Price × Quantity = P × 50
Calculating New Price
1. New price after a 30% increase = P + 0.30P = 1.30P
Calculating New Expenditure
1. New expenditure (E2) = 1.20 × Initial Expenditure = 1.20 × E1 = 1.20 × (P × 50) = 60P
Finding New Consumption
1. Let the new consumption be X kg.
2. New expenditure can also be expressed as: New Expenditure = New Price × New Consumption
3. Therefore, 60P = (1.30P) × X
Solving for X
1. Cancel P from both sides (assuming P is not zero):
60 = 1.30X
2. Rearranging gives:
X = 60 / 1.30
3. Calculating X:
X ≈ 46.15 kg
Since we are looking for an approximate value, the new consumption of the family is about 46 kg.
Conclusion
The new consumption of rice by the family is approximately 46 kg, making the correct answer option D.
To find the new consumption of rice by the family after a price increase, we will analyze the changes in expenditure and price.
Initial Information
- Initial Consumption: 50 kg of rice
- Price Increase: 30%
- Expenditure Increase: 20%
Calculating Initial Expenditure
1. Let the initial price of rice be P per kg.
2. Initial expenditure (E1) = Price × Quantity = P × 50
Calculating New Price
1. New price after a 30% increase = P + 0.30P = 1.30P
Calculating New Expenditure
1. New expenditure (E2) = 1.20 × Initial Expenditure = 1.20 × E1 = 1.20 × (P × 50) = 60P
Finding New Consumption
1. Let the new consumption be X kg.
2. New expenditure can also be expressed as: New Expenditure = New Price × New Consumption
3. Therefore, 60P = (1.30P) × X
Solving for X
1. Cancel P from both sides (assuming P is not zero):
60 = 1.30X
2. Rearranging gives:
X = 60 / 1.30
3. Calculating X:
X ≈ 46.15 kg
Since we are looking for an approximate value, the new consumption of the family is about 46 kg.
Conclusion
The new consumption of rice by the family is approximately 46 kg, making the correct answer option D.
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Question Description
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