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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?
Most Upvoted Answer
A reduction of 20% in the price of rice enables a housewife to buy 5 k...
Understanding the Problem
A housewife can buy more rice after a 20% price reduction. We need to determine the new price per kg of rice after this reduction.
Initial Setup
- Let the original price of rice per kg be "P".
- After a 20% reduction, the new price becomes 0.8P.
- The housewife spends 1200 rupees.
Equations Setup
- Originally, for 1200 rupees, she could buy 1200/P kg of rice.
- After the price reduction, she can buy 1200/(0.8P) kg of rice.
Difference in Quantity
- The difference in quantity purchased is given as 5 kg:
1200/(0.8P) - 1200/P = 5
Solving the Equation
1. Simplify the left-hand side:
- Find a common denominator: (0.8P)(P) = 0.8P².
- The equation becomes:
(1200P - 1200 * 0.8P) / (0.8P²) = 5
2. This simplifies to:
(1200P - 960P) / (0.8P²) = 5
- Resulting in:
240P / (0.8P²) = 5
3. Cross-multiplying gives:
240P = 5 * 0.8P²
4. Rearranging leads to:
0.8P² - 240P = 0
Factoring
- Factoring out P:
P(0.8P - 240) = 0
- This implies:
0.8P = 240 => P = 240 / 0.8 = 300
Finding the Reduced Price
- The reduced price per kg is:
0.8P = 0.8 * 300 = 240
- Therefore, the reduced price per kg of rice is:
240 / 5 = 48
Conclusion
The reduced price per kg of rice is 48 rupees, confirming that the correct answer is option 'C'.
A housewife can buy more rice after a 20% price reduction. We need to determine the new price per kg of rice after this reduction.
Initial Setup
- Let the original price of rice per kg be "P".
- After a 20% reduction, the new price becomes 0.8P.
- The housewife spends 1200 rupees.
Equations Setup
- Originally, for 1200 rupees, she could buy 1200/P kg of rice.
- After the price reduction, she can buy 1200/(0.8P) kg of rice.
Difference in Quantity
- The difference in quantity purchased is given as 5 kg:
1200/(0.8P) - 1200/P = 5
Solving the Equation
1. Simplify the left-hand side:
- Find a common denominator: (0.8P)(P) = 0.8P².
- The equation becomes:
(1200P - 1200 * 0.8P) / (0.8P²) = 5
2. This simplifies to:
(1200P - 960P) / (0.8P²) = 5
- Resulting in:
240P / (0.8P²) = 5
3. Cross-multiplying gives:
240P = 5 * 0.8P²
4. Rearranging leads to:
0.8P² - 240P = 0
Factoring
- Factoring out P:
P(0.8P - 240) = 0
- This implies:
0.8P = 240 => P = 240 / 0.8 = 300
Finding the Reduced Price
- The reduced price per kg is:
0.8P = 0.8 * 300 = 240
- Therefore, the reduced price per kg of rice is:
240 / 5 = 48
Conclusion
The reduced price per kg of rice is 48 rupees, confirming that the correct answer is option 'C'.
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Community Answer
A reduction of 20% in the price of rice enables a housewife to buy 5 k...
Step-by-Step Solution
- Define Variables:
- Let p = Original price per kg of rice (₹)
- Reduced price = 20% less than original price = 0.8p
- Determine Quantity Purchased:
- With original price:
- Quantity bought = Total Money / Original Price = ₹1,200 / p = 1200/p kg
- With reduced price:
- Quantity bought = Total Money / Reduced Price = ₹1,200 / (0.8p) = 1500/p kg
- With original price:
- Set Up the Equation Based on the Increase in Quantity:
- Difference in quantity = 5 kg
- Therefore, 1500/p - 1200/p = 5
- Simplify the equation:
- 300/p = 5
- Solve for p:
- p = 300 / 5 = ₹60
- Calculate the Reduced Price:
- Reduced price = 0.8 x Original price = 0.8 x ₹60 = ₹48
Conclusion
The reduced price per kg of rice is ₹48, which corresponds to Option c).
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