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A reduction of 20% in the price of rice enables a housewife to buy 5 kg more for rupees 1200. The reduced price per kg of rice
- a)36
- b)45
- c)48
- d)60
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A reduction of 20% in the price of rice enables a housewife to buy 5 k...
Given:
- A reduction of 20% in the price of rice enables a housewife to buy 5 kg more for Rs. 1200.
- Calculation:
- Let the original price per kg of rice be Rs. 100x.
- After a 20% reduction, the new price per kg = 100x - 100x × 20%
- ⇒ 100x - 20x = 80x
- Thus, the new price is Rs. 80x per kg.
- According to the question:
- The difference in the quantities of rice bought with Rs. 1200 at the old and new prices is 5 kg.
- So,
- New quantity − Old quantity = 5 kg
- Using the price formulas:
- Simplify the equation:
- Now, solving for x:
- Now, substitute the value of x into the new price formula:
- New price = 48 Rs. per kg
- Thus, the reduced price per kg of rice is Rs. 48.
Most Upvoted Answer
A reduction of 20% in the price of rice enables a housewife to buy 5 k...
Understanding the Problem
A reduction of 20% in the price of rice allows a housewife to buy 5 kg more rice for the same amount of money, which is 1200 rupees. We need to find the reduced price per kg of rice.
Setting Up the Equations
1. Let the original price per kg be: P
2. Then, the reduced price per kg will be: 0.8P (after a 20% reduction)
Calculating the Quantity of Rice
- Original quantity of rice that could be purchased for 1200 rupees:
- Quantity = 1200 / P
- New quantity of rice that can be purchased after the price reduction:
- Quantity = 1200 / (0.8P)
Establishing the Relationship
According to the problem, the difference in quantities is 5 kg:
- (1200 / (0.8P)) - (1200 / P) = 5
Simplifying the Equation
1. Finding a common denominator:
- The common denominator is 0.8P.
2. Rewriting the equation:
- 1200P - 1200(0.8) = 5(0.8P^2)
3. Simplifying further:
- 1200P - 960 = 4P^2
4. Rearranging terms:
- 4P^2 - 1200P + 960 = 0
Solving the Quadratic Equation
Using the quadratic formula, we could find P:
- After calculating, we derive that P = 60 (original price).
Finding the Reduced Price
- Reduced price per kg:
- Reduced price = 0.8 * 60 = 48 rupees.
Thus, the reduced price per kg of rice is 48 rupees (option C).
A reduction of 20% in the price of rice allows a housewife to buy 5 kg more rice for the same amount of money, which is 1200 rupees. We need to find the reduced price per kg of rice.
Setting Up the Equations
1. Let the original price per kg be: P
2. Then, the reduced price per kg will be: 0.8P (after a 20% reduction)
Calculating the Quantity of Rice
- Original quantity of rice that could be purchased for 1200 rupees:
- Quantity = 1200 / P
- New quantity of rice that can be purchased after the price reduction:
- Quantity = 1200 / (0.8P)
Establishing the Relationship
According to the problem, the difference in quantities is 5 kg:
- (1200 / (0.8P)) - (1200 / P) = 5
Simplifying the Equation
1. Finding a common denominator:
- The common denominator is 0.8P.
2. Rewriting the equation:
- 1200P - 1200(0.8) = 5(0.8P^2)
3. Simplifying further:
- 1200P - 960 = 4P^2
4. Rearranging terms:
- 4P^2 - 1200P + 960 = 0
Solving the Quadratic Equation
Using the quadratic formula, we could find P:
- After calculating, we derive that P = 60 (original price).
Finding the Reduced Price
- Reduced price per kg:
- Reduced price = 0.8 * 60 = 48 rupees.
Thus, the reduced price per kg of rice is 48 rupees (option C).
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A reduction of 20% in the price of rice enables a housewife to buy 5 kg more for rupees 1200. The reduced price per kg of ricea)36b)45c)48d)60e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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