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A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg?
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A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg ...
Problem:
A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture?
Solution:
Let the quantities of rice of the three varieties be x, y and z kg respectively.
Cost price of x kg of first variety of rice = Rs. 20x
Cost price of y kg of second variety of rice = Rs. 24y
Cost price of z kg of third variety of rice = Rs. 30z
Total cost price of the mixture = 20x + 24y + 30z
Given that the merchant sells the mixture at Rs. 30/kg with a profit of 20%.
Therefore, selling price of the mixture = 1.20*(20x + 24y + 30z)
Selling price of 1 kg of the mixture = Rs. 30
Therefore, 1.20*(20x + 24y + 30z)/(x+y+z) = 30
Simplifying the above equation, we get:
24x + 28.8y + 36z = 30(x+y+z)
24x + 28.8y + 36z = 30x + 30y + 30z
6x - 1.2y - 6z = 0
Simplifying again, we get:
5x = y + 5z
Given that 2 kg of the third variety is there in the mixture, i.e., z=2.
Substituting z=2 in the above equation, we get:
5x = y + 10
Therefore, y = 5x - 10
We need to find the value of y, i.e., the quantity of the second variety of rice in the mixture.
We know that x + y + z = total quantity of rice in the mixture.
Substituting z=2 and y=5x-10 in the above equation, we get:
x + (5x-10) + 2 = x + y + z
Simplifying, we get:
6x = 8
Therefore, x=4/3 kg and y=5x-10=6.67 kg (approx.)
Hence, the quantity of the second variety of rice in the mixture is approximately 6.67 kg.
Answer: Option 2.3 kg.
A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture?
Solution:
Let the quantities of rice of the three varieties be x, y and z kg respectively.
Cost price of x kg of first variety of rice = Rs. 20x
Cost price of y kg of second variety of rice = Rs. 24y
Cost price of z kg of third variety of rice = Rs. 30z
Total cost price of the mixture = 20x + 24y + 30z
Given that the merchant sells the mixture at Rs. 30/kg with a profit of 20%.
Therefore, selling price of the mixture = 1.20*(20x + 24y + 30z)
Selling price of 1 kg of the mixture = Rs. 30
Therefore, 1.20*(20x + 24y + 30z)/(x+y+z) = 30
Simplifying the above equation, we get:
24x + 28.8y + 36z = 30(x+y+z)
24x + 28.8y + 36z = 30x + 30y + 30z
6x - 1.2y - 6z = 0
Simplifying again, we get:
5x = y + 5z
Given that 2 kg of the third variety is there in the mixture, i.e., z=2.
Substituting z=2 in the above equation, we get:
5x = y + 10
Therefore, y = 5x - 10
We need to find the value of y, i.e., the quantity of the second variety of rice in the mixture.
We know that x + y + z = total quantity of rice in the mixture.
Substituting z=2 and y=5x-10 in the above equation, we get:
x + (5x-10) + 2 = x + y + z
Simplifying, we get:
6x = 8
Therefore, x=4/3 kg and y=5x-10=6.67 kg (approx.)
Hence, the quantity of the second variety of rice in the mixture is approximately 6.67 kg.
Answer: Option 2.3 kg.
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A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg?
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A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg?.
A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg and Rs. 30/kg, and sells the mixture at Rs. 30/kg with a profit of 20%. How many kilograms of the second variety will be in the mixture, if 2 kg of the third variety is there in the mixture? 1.1 kg 2.3 kg 3.5 kg 4.6 kg?.
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