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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?
Verified Answer
A merchant mixes three varieties of rice costing Rs. 20/kg, Rs. 24/kg ...
The merchant sells the mixture at Rs. 30/kg with a profit of 20%, so the cost price of the mixture is 30 / (1 + 20/100) = Rs. 25/kg.
Since the mixture contains 2 kg of the third variety of rice, which costs Rs. 30/kg, the total cost of the mixture is 2 * 30 = Rs. 60.
The remaining part of the mixture consists of the first and second varieties of rice, which cost Rs. 20/kg and Rs. 24/kg, respectively. The total cost of these two varieties is 25 - 60 = -35.
Since the second variety of rice costs Rs. 24/kg, the weight of the second variety in the mixture is -35 / 24 = 1.46 kg.
The weight of the second variety in the mixture is 1.46 kg, which is approximately 1.5 kg. Therefore, the answer is 3: 1.5 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:
Step 1: Calculate the cost price of the mixture
Let the quantity of rice of the first variety, second variety and third variety be x, y and 2 kg respectively.
The cost price of the mixture = (20x + 24y + 30 x 2) / (x + y + 2) = (20x + 24y + 60) / (x + y + 2)
Step 2: Calculate the selling price of the mixture
The selling price of the mixture = Rs. 30/kg
Let the quantity of the mixture be z kg.
Therefore, the selling price of the mixture = 30z
Step 3: Calculate the profit percentage
Profit percentage = (Selling price - Cost price) / Cost price x 100
Given, profit percentage = 20%
Therefore, (30z - (20x + 24y + 60) / (x + y + 2)) / ((20x + 24y + 60) / (x + y + 2)) x 100 = 20
Step 4: Simplify the expression
On simplification, we get:
y = 3x
Step 5: Substitute the value of y in the expression for cost price
Cost price of the mixture = (20x + 24y + 60) / (x + y + 2)
= (20x + 24(3x) + 60) / (x + 3x + 2)
= (68x + 60) / (4x + 2)
= (34x + 30) / (2x + 1)
Step 6: Substitute the values of cost price and selling price in the expression for profit percentage to get the value of x
(30z - (34x + 30) / (2x + 1)) / ((34x + 30) / (2x + 1)) x 100 = 20
On simplification, we get:
x = 3
Therefore, y = 9
Step 7: Calculate the quantity of the second variety in the mixture
The quantity of the second variety in the mixture = 9 kg
Answer: Therefore, 9 kg of the second variety will be in the mixture if 2 kg of the third variety is there in the mixture.
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:
Step 1: Calculate the cost price of the mixture
Let the quantity of rice of the first variety, second variety and third variety be x, y and 2 kg respectively.
The cost price of the mixture = (20x + 24y + 30 x 2) / (x + y + 2) = (20x + 24y + 60) / (x + y + 2)
Step 2: Calculate the selling price of the mixture
The selling price of the mixture = Rs. 30/kg
Let the quantity of the mixture be z kg.
Therefore, the selling price of the mixture = 30z
Step 3: Calculate the profit percentage
Profit percentage = (Selling price - Cost price) / Cost price x 100
Given, profit percentage = 20%
Therefore, (30z - (20x + 24y + 60) / (x + y + 2)) / ((20x + 24y + 60) / (x + y + 2)) x 100 = 20
Step 4: Simplify the expression
On simplification, we get:
y = 3x
Step 5: Substitute the value of y in the expression for cost price
Cost price of the mixture = (20x + 24y + 60) / (x + y + 2)
= (20x + 24(3x) + 60) / (x + 3x + 2)
= (68x + 60) / (4x + 2)
= (34x + 30) / (2x + 1)
Step 6: Substitute the values of cost price and selling price in the expression for profit percentage to get the value of x
(30z - (34x + 30) / (2x + 1)) / ((34x + 30) / (2x + 1)) x 100 = 20
On simplification, we get:
x = 3
Therefore, y = 9
Step 7: Calculate the quantity of the second variety in the mixture
The quantity of the second variety in the mixture = 9 kg
Answer: Therefore, 9 kg of the second variety will be in the mixture if 2 kg of the third variety is there in the mixture.
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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?
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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? 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? 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?.
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? 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? 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?.
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