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In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?
- a)7 : 20 : 7
- b)4 : 8 : 13
- c)5 : 5 : 21
- d)5 : 9 : 21
- e)7 : 7 : 20
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and R...
E) 7 : 7 : 20
Explanation: SP = 63.8, Profit=10%, so CP = (100/110)*63.8 = 58 Now 58 is greater than 42 and 54 and less than 65 So 42 65
. 58
7 16
And 54 65
. 58
7 4
So 1 part of 1st wheat A, 1 part of 2nd wheat B and 2 parts of 3rd wheat C gives A : C = 7 : 16, and B : C = 7 : 4 So A : B : C = 7 : 7 : (16+4) *we have taken 2 parts of C so it is added – when there are 3 varieties to be mixed it is not done like simple calculation of A : C and B : C
Explanation: SP = 63.8, Profit=10%, so CP = (100/110)*63.8 = 58 Now 58 is greater than 42 and 54 and less than 65 So 42 65
. 58
7 16
And 54 65
. 58
7 4
So 1 part of 1st wheat A, 1 part of 2nd wheat B and 2 parts of 3rd wheat C gives A : C = 7 : 16, and B : C = 7 : 4 So A : B : C = 7 : 7 : (16+4) *we have taken 2 parts of C so it is added – when there are 3 varieties to be mixed it is not done like simple calculation of A : C and B : C
Most Upvoted Answer
In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and R...
To find the ratio in which the three varieties of wheat should be mixed, we need to consider the costs and the desired selling price.
Let's assume the quantities of the three varieties of wheat as x, y, and z respectively.
Cost Calculation:
The cost of variety 1 (Rs 42) per unit is 42x.
The cost of variety 2 (Rs 54) per unit is 54y.
The cost of variety 3 (Rs 65) per unit is 65z.
The total cost of the mixture is the sum of the costs of the three varieties:
Total Cost = 42x + 54y + 65z
Selling Price Calculation:
We want to sell the mixture at a selling price of Rs 63.8 per unit, which includes a profit of 10%.
So, the cost price per unit is (100/110) * Rs 63.8 = Rs 58.
Now, we can equate the selling price to the cost price to find the ratio:
42x + 54y + 65z = 58(x + y + z)
Simplifying the equation:
42x + 54y + 65z = 58x + 58y + 58z
42x - 58x + 54y - 58y + 65z - 58z = 0
-16x - 4y + 7z = 0
Ratio Calculation:
To find a suitable ratio, we need to find integer values for x, y, and z that satisfy the equation -16x - 4y + 7z = 0.
Let's try different values of z and find corresponding values of x and y.
When z = 7, the equation becomes:
-16x - 4y + 7(7) = 0
-16x - 4y + 49 = 0
-16x - 4y = -49
By trying different values, we find that x = -3 and y = 1 satisfy the equation. However, we need positive values for the quantities.
So, let's try z = 14. The equation becomes:
-16x - 4y + 7(14) = 0
-16x - 4y + 98 = 0
-16x - 4y = -98
By trying different values, we find that x = -5 and y = -2 satisfy the equation. Again, we need positive values for the quantities.
Finally, let's try z = 21. The equation becomes:
-16x - 4y + 7(21) = 0
-16x - 4y + 147 = 0
-16x - 4y = -147
By trying different values, we find that x = -7 and y = -4 satisfy the equation. Again, we need positive values for the quantities.
Hence, the suitable ratio is x : y : z = 7 : 7 : 20, which is option E.
Let's assume the quantities of the three varieties of wheat as x, y, and z respectively.
Cost Calculation:
The cost of variety 1 (Rs 42) per unit is 42x.
The cost of variety 2 (Rs 54) per unit is 54y.
The cost of variety 3 (Rs 65) per unit is 65z.
The total cost of the mixture is the sum of the costs of the three varieties:
Total Cost = 42x + 54y + 65z
Selling Price Calculation:
We want to sell the mixture at a selling price of Rs 63.8 per unit, which includes a profit of 10%.
So, the cost price per unit is (100/110) * Rs 63.8 = Rs 58.
Now, we can equate the selling price to the cost price to find the ratio:
42x + 54y + 65z = 58(x + y + z)
Simplifying the equation:
42x + 54y + 65z = 58x + 58y + 58z
42x - 58x + 54y - 58y + 65z - 58z = 0
-16x - 4y + 7z = 0
Ratio Calculation:
To find a suitable ratio, we need to find integer values for x, y, and z that satisfy the equation -16x - 4y + 7z = 0.
Let's try different values of z and find corresponding values of x and y.
When z = 7, the equation becomes:
-16x - 4y + 7(7) = 0
-16x - 4y + 49 = 0
-16x - 4y = -49
By trying different values, we find that x = -3 and y = 1 satisfy the equation. However, we need positive values for the quantities.
So, let's try z = 14. The equation becomes:
-16x - 4y + 7(14) = 0
-16x - 4y + 98 = 0
-16x - 4y = -98
By trying different values, we find that x = -5 and y = -2 satisfy the equation. Again, we need positive values for the quantities.
Finally, let's try z = 21. The equation becomes:
-16x - 4y + 7(21) = 0
-16x - 4y + 147 = 0
-16x - 4y = -147
By trying different values, we find that x = -7 and y = -4 satisfy the equation. Again, we need positive values for the quantities.
Hence, the suitable ratio is x : y : z = 7 : 7 : 20, which is option E.
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In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer?
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In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer?.
In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what ratio must the 3 varieties of wheat costing Rs 42, Rs 54 and Rs 65 respectively be mixed so that the resulting mixture is sold for Rs 63.8 at a profit of 10%?a)7 : 20 : 7b)4 : 8 : 13c)5 : 5 : 21d)5 : 9 : 21e)7 : 7 : 20Correct answer is option 'E'. Can you explain this answer?.
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