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McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?
- a)3 : 2
- b)13 : 18
- c)2 : 3
- d)8 : 11
Correct answer is option 'A'. Can you explain this answer?
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McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A...
Total amount which McGrath gets after selling the 100 kg of rice = Rs. 1,100
And profit = Rs. 300
∴ CP of 100 kg = 1,100 - 300 = Rs. 800
CP of 1 kg = Rs. 8
Now, apply the rule of alligation:
Hence, ratio of A and B in the mixture = 3 : 2
And profit = Rs. 300
∴ CP of 100 kg = 1,100 - 300 = Rs. 800
CP of 1 kg = Rs. 8
Now, apply the rule of alligation:
Hence, ratio of A and B in the mixture = 3 : 2
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McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A...
To solve this problem, we need to use the concept of weighted average. Let's assume that the proportion of A type rice in the mixture is 'x' and the proportion of B type rice is 'y'.
We know that the total weight of the mixture is 100 kg, so we can write the equation:
x + y = 100 - (1)
We are also given that the cost price of A type rice is Rs. 10 per kg and the cost price of B type rice is Rs. 5 per kg.
Let's calculate the total cost price of the mixture. Since the total weight of the mixture is 100 kg, the total cost price can be calculated as:
10x + 5y = 1100 - (2)
We are also given that McGrath earned a profit of Rs. 300 by selling the mixture. The selling price can be calculated as:
Selling price = Cost price + Profit
1100 = 10x + 5y + 300
800 = 10x + 5y - (3)
Now we have a system of equations (1), (2), and (3) that we can solve to find the values of x and y.
Multiplying equation (1) by 5, we get:
5x + 5y = 500 - (4)
Subtracting equation (4) from equation (2), we get:
10x + 5y - (5x + 5y) = 1100 - 500
5x = 600
x = 120
Substituting the value of x in equation (1), we get:
120 + y = 100
y = -20
Since the proportion cannot be negative, we discard this solution.
Therefore, the only valid solution is x = 120 and y = 100 - x = 100 - 120 = -20.
Hence, the proportion of A and B types of rice in the mixture is 120 : -20, which simplifies to 6 : -1.
To make the proportion positive, we can multiply both sides by -1:
-6 : 1
Since we are asked for the proportion in terms of positive numbers, the final answer is:
6 : 1
Therefore, the correct answer is option A) 6 : 1.
We know that the total weight of the mixture is 100 kg, so we can write the equation:
x + y = 100 - (1)
We are also given that the cost price of A type rice is Rs. 10 per kg and the cost price of B type rice is Rs. 5 per kg.
Let's calculate the total cost price of the mixture. Since the total weight of the mixture is 100 kg, the total cost price can be calculated as:
10x + 5y = 1100 - (2)
We are also given that McGrath earned a profit of Rs. 300 by selling the mixture. The selling price can be calculated as:
Selling price = Cost price + Profit
1100 = 10x + 5y + 300
800 = 10x + 5y - (3)
Now we have a system of equations (1), (2), and (3) that we can solve to find the values of x and y.
Multiplying equation (1) by 5, we get:
5x + 5y = 500 - (4)
Subtracting equation (4) from equation (2), we get:
10x + 5y - (5x + 5y) = 1100 - 500
5x = 600
x = 120
Substituting the value of x in equation (1), we get:
120 + y = 100
y = -20
Since the proportion cannot be negative, we discard this solution.
Therefore, the only valid solution is x = 120 and y = 100 - x = 100 - 120 = -20.
Hence, the proportion of A and B types of rice in the mixture is 120 : -20, which simplifies to 6 : -1.
To make the proportion positive, we can multiply both sides by -1:
-6 : 1
Since we are asked for the proportion in terms of positive numbers, the final answer is:
6 : 1
Therefore, the correct answer is option A) 6 : 1.
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McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer?
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McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer?.
McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1,100. What was the proportion of A and B types of rice in the mixture if the cost prices of A and B are Rs. 10 and Rs. 5 per kg, respectively?a)3 : 2b)13 : 18c)2 : 3d)8 : 11Correct answer is option 'A'. Can you explain this answer?.
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