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How many kilograms of rice costing Rs. 30/kg should be mixed with 40 kg of rice costing Rs. 45/kg, so that there will be a profit of 25% on selling the mixture at Rs. 50/kg?
  • a)
    10 kg
  • b)
    15 kg
  • c)
    20 kg
  • d)
    25 kg
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many kilograms of rice costing Rs. 30/kg should be mixed with 40 k...
Cost price of resultant rice = 50/1.25 = 40

5 : 10 = 1 : 2

Hence, Option C is correct.
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How many kilograms of rice costing Rs. 30/kg should be mixed with 40 k...
Problem Overview
To determine how many kilograms of rice costing Rs. 30/kg should be mixed with 40 kg of rice costing Rs. 45/kg to achieve a 25% profit when selling the mixture at Rs. 50/kg.
Step 1: Calculate Selling Price and Cost Price
- Selling Price (SP) of the mixture per kg = Rs. 50
- Desired Profit = 25%
- Therefore, Cost Price (CP) of the mixture = SP / (1 + Profit%) = 50 / 1.25 = Rs. 40/kg
Step 2: Cost of the Rice Mixture
Let x = kg of rice at Rs. 30/kg.
- Cost of x kg of rice = 30x
- Cost of 40 kg of rice at Rs. 45/kg = 45 * 40 = Rs. 1800
- Total cost of the mixture = 30x + 1800
- Total weight of the mixture = x + 40 kg
Step 3: Cost Price Equation
To find x, set the total cost equal to the total cost price of the mixture.
CP = Total Cost / Total Weight
Thus,
(30x + 1800) / (x + 40) = 40
Step 4: Solve the Equation
Cross-multiplying gives:
30x + 1800 = 40(x + 40)
Expanding the right side:
30x + 1800 = 40x + 1600
Rearranging the equation:
1800 - 1600 = 40x - 30x
So,
200 = 10x
This gives:
x = 20 kg
Conclusion
Therefore, the amount of rice costing Rs. 30/kg that should be mixed is 20 kg.
Correct answer is option 'C'.
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Question Description
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