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In two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?
- a)8 kg and 20 kg
- b)4 kg and 24 kg
- c)3 kg and 25 kg
- d)7 kg and 21 kg
Correct answer is option 'D'. Can you explain this answer?
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In two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many k...
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Problem Analysis:
We are given two alloys with copper to zinc ratios of 5:2 and 3:4. We need to find out how much of each alloy we need to melt together to obtain 28 kg of a new alloy with an equal amount of copper and zinc.
Given Data:
- The ratio of Copper to Zinc in Alloy 1 = 5:2
- The ratio of Copper to Zinc in Alloy 2 = 3:4
- Total mass of the new alloy = 28 kg
To solve this problem, we can use the method of alligation. Let's see how.
Solution:
Step 1: Find the ratio of Copper to Zinc in the new alloy.
Since the new alloy has an equal amount of copper and zinc, the ratio of copper to zinc in the new alloy will be 1:1.
Step 2: Use alligation to find the ratio of the two alloys.
Let's draw a diagram for alligation with the ratios of copper to zinc in the two alloys.
Ratio of Copper to Zinc in Alloy 1 = 5:2
Ratio of Copper to Zinc in Alloy 2 = 3:4
Ratio of Copper to Zinc in the new alloy = 1:1
We need to find out how much of each alloy we need to mix to get the new alloy. Let's assume we need x kg of Alloy 1 and y kg of Alloy 2.
5:2 1:1 3:4
| | |
x | y
| | |
-------|-------
28 kg
To find out the values of x and y, we can add the values in each column and equate them to the total mass of the new alloy.
For copper:
5x + 3y = 28
For zinc:
2x + 4y = 28
Step 3: Solve the equations to find x and y.
Let's solve the two equations simultaneously.
5x + 3y = 28
2x + 4y = 28
Multiplying the first equation by 2 and subtracting the second equation, we get:
10x + 6y - 4x - 8y = 56 - 28
6x = 28
x = 7
Substituting the value of x in any of the equations, we get:
5x + 3y = 28
35 + 3y = 28
3y = 28 - 35
y = 7
Therefore, we need 7 kg of Alloy 1 and 21 kg of Alloy 2 to obtain 28 kg of a new alloy with an equal amount of copper and zinc.
Answer: (D) 7 kg and 21 kg
We are given two alloys with copper to zinc ratios of 5:2 and 3:4. We need to find out how much of each alloy we need to melt together to obtain 28 kg of a new alloy with an equal amount of copper and zinc.
Given Data:
- The ratio of Copper to Zinc in Alloy 1 = 5:2
- The ratio of Copper to Zinc in Alloy 2 = 3:4
- Total mass of the new alloy = 28 kg
To solve this problem, we can use the method of alligation. Let's see how.
Solution:
Step 1: Find the ratio of Copper to Zinc in the new alloy.
Since the new alloy has an equal amount of copper and zinc, the ratio of copper to zinc in the new alloy will be 1:1.
Step 2: Use alligation to find the ratio of the two alloys.
Let's draw a diagram for alligation with the ratios of copper to zinc in the two alloys.
Ratio of Copper to Zinc in Alloy 1 = 5:2
Ratio of Copper to Zinc in Alloy 2 = 3:4
Ratio of Copper to Zinc in the new alloy = 1:1
We need to find out how much of each alloy we need to mix to get the new alloy. Let's assume we need x kg of Alloy 1 and y kg of Alloy 2.
5:2 1:1 3:4
| | |
x | y
| | |
-------|-------
28 kg
To find out the values of x and y, we can add the values in each column and equate them to the total mass of the new alloy.
For copper:
5x + 3y = 28
For zinc:
2x + 4y = 28
Step 3: Solve the equations to find x and y.
Let's solve the two equations simultaneously.
5x + 3y = 28
2x + 4y = 28
Multiplying the first equation by 2 and subtracting the second equation, we get:
10x + 6y - 4x - 8y = 56 - 28
6x = 28
x = 7
Substituting the value of x in any of the equations, we get:
5x + 3y = 28
35 + 3y = 28
3y = 28 - 35
y = 7
Therefore, we need 7 kg of Alloy 1 and 21 kg of Alloy 2 to obtain 28 kg of a new alloy with an equal amount of copper and zinc.
Answer: (D) 7 kg and 21 kg
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In two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?a)8 kg and 20 kgb)4 kg and 24 kgc)3 kg and 25 kgd)7 kg and 21 kgCorrect answer is option 'D'. Can you explain this answer?
Question Description
In two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?a)8 kg and 20 kgb)4 kg and 24 kgc)3 kg and 25 kgd)7 kg and 21 kgCorrect answer is option 'D'. 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 two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?a)8 kg and 20 kgb)4 kg and 24 kgc)3 kg and 25 kgd)7 kg and 21 kgCorrect answer is option 'D'. 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 two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?a)8 kg and 20 kgb)4 kg and 24 kgc)3 kg and 25 kgd)7 kg and 21 kgCorrect answer is option 'D'. Can you explain this answer?.
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Solutions for In two alloys, the ratios of copper to zinc is 5:2 and 3:4. How many kilograms of the first alloy and the second alloy respectively should be melted together to obtain 28 kg of a new alloy with equal copper and zinc?a)8 kg and 20 kgb)4 kg and 24 kgc)3 kg and 25 kgd)7 kg and 21 kgCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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