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Two metals contain zinc and copper in the ratio 2:1 and 4:1 respectively. In what ratio these two must be mixed to get a new metal containing zinc and copper in the ratio 3:1?
  • a)
    3:5   
  • b)
    4:5   
  • c)
    2:3 
  • d)
    4:1
Correct answer is option 'A'. Can you explain this answer?
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Two metals contain zinc and copper in the ratio 2:1 and 4:1 respective...
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Two metals contain zinc and copper in the ratio 2:1 and 4:1 respective...
Given:
- Ratio of zinc to copper in first metal = 2:1
- Ratio of zinc to copper in second metal = 4:1
- Ratio of zinc to copper in new metal required = 3:1

To find:
- Ratio in which the two metals must be mixed to obtain the new metal

Solution:
Let the first metal contain 2x units of zinc and x units of copper.
Let the second metal contain 4y units of zinc and y units of copper.

To obtain the new metal, we need to mix these two metals in such a way that the ratio of zinc to copper becomes 3:1. This means that the total amount of zinc and copper in the new metal must be in the ratio 3:1. Hence, we can write:

2x + 4y : x + y = 3 : 1

Cross-multiplying and simplifying, we get:

6x + 12y = 3x + 3y
=> 3x = 9y
=> x/y = 3/1

Therefore, the first metal and the second metal must be mixed in the ratio 3:1 to obtain the new metal with zinc and copper in the ratio 3:1.

Answer:
Option (a) 3:5
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