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A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed?
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A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21...
The Problem
A shopkeeper mixed three varieties of wheat costing Rs 12 per kg, Rs 18 per kg, and Rs 21 per kg, respectively. The mixture was sold at Rs 15 per kg with a 20% profit. We need to determine the possible ratio of the varieties mixed.
Understanding the Problem
To solve this problem, we need to find the ratio of the three varieties of wheat in the mixture. Since the cost and selling price of the mixture are given, we can use the concept of weighted averages to find the ratio.
Solution
To find the ratio of the three varieties of wheat, we will follow these steps:
Step 1: Formulating the Equation
Let's assume the ratio of the three varieties of wheat is x:y:z.
According to the problem, the cost price of the mixture is the weighted average of the three varieties of wheat, and the selling price includes a 20% profit.
The weighted average formula for the cost price is:
(12x + 18y + 21z)/(x + y + z)
The selling price includes a 20% profit, which means it is 120% of the cost price. Therefore, the selling price is:
1.2 * [(12x + 18y + 21z)/(x + y + z)]
We know that the selling price is Rs 15 per kg. So, we can set up the equation:
1.2 * [(12x + 18y + 21z)/(x + y + z)] = 15
Step 2: Simplifying the Equation
Let's simplify the equation to make it easier to solve:
1.2 * (12x + 18y + 21z) = 15 * (x + y + z)
Simplifying further, we get:
14.4x + 21.6y + 25.2z = 15x + 15y + 15z
14.4x - 15x + 21.6y - 15y + 25.2z - 15z = 0
-0.6x + 6.6y + 10.2z = 0
Step 3: Finding the Possible Ratio
To find the possible ratio, we need to find values of x, y, and z that satisfy the equation -0.6x + 6.6y + 10.2z = 0.
Since there are infinitely many solutions to this equation, we can set one variable as a parameter and express the other variables in terms of that parameter.
Let's assume x = k, where k is a parameter.
From the equation, we can express y in terms of x:
-0.6k + 6.6y + 10.2z = 0
6.6y = 0.6k - 10.2z
y = (0.6k - 10.2z)/6.6
Similarly, we can express z in terms of x:
-0.6k + 6.6y + 10.2z = 0
10.2z = 0.6k - 6.6y
z = (0.6k - 6
A shopkeeper mixed three varieties of wheat costing Rs 12 per kg, Rs 18 per kg, and Rs 21 per kg, respectively. The mixture was sold at Rs 15 per kg with a 20% profit. We need to determine the possible ratio of the varieties mixed.
Understanding the Problem
To solve this problem, we need to find the ratio of the three varieties of wheat in the mixture. Since the cost and selling price of the mixture are given, we can use the concept of weighted averages to find the ratio.
Solution
To find the ratio of the three varieties of wheat, we will follow these steps:
Step 1: Formulating the Equation
Let's assume the ratio of the three varieties of wheat is x:y:z.
According to the problem, the cost price of the mixture is the weighted average of the three varieties of wheat, and the selling price includes a 20% profit.
The weighted average formula for the cost price is:
(12x + 18y + 21z)/(x + y + z)
The selling price includes a 20% profit, which means it is 120% of the cost price. Therefore, the selling price is:
1.2 * [(12x + 18y + 21z)/(x + y + z)]
We know that the selling price is Rs 15 per kg. So, we can set up the equation:
1.2 * [(12x + 18y + 21z)/(x + y + z)] = 15
Step 2: Simplifying the Equation
Let's simplify the equation to make it easier to solve:
1.2 * (12x + 18y + 21z) = 15 * (x + y + z)
Simplifying further, we get:
14.4x + 21.6y + 25.2z = 15x + 15y + 15z
14.4x - 15x + 21.6y - 15y + 25.2z - 15z = 0
-0.6x + 6.6y + 10.2z = 0
Step 3: Finding the Possible Ratio
To find the possible ratio, we need to find values of x, y, and z that satisfy the equation -0.6x + 6.6y + 10.2z = 0.
Since there are infinitely many solutions to this equation, we can set one variable as a parameter and express the other variables in terms of that parameter.
Let's assume x = k, where k is a parameter.
From the equation, we can express y in terms of x:
-0.6k + 6.6y + 10.2z = 0
6.6y = 0.6k - 10.2z
y = (0.6k - 10.2z)/6.6
Similarly, we can express z in terms of x:
-0.6k + 6.6y + 10.2z = 0
10.2z = 0.6k - 6.6y
z = (0.6k - 6
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A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed?
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A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed?.
A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper mixed 3 varieties of wheat costing rs 12 per kg 18 and 21 per kg respectively and sold the mixture at rs 15 per kg at 20% profit. which of the following represents a possible ratio of the varieties mixed?.
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