An alloy contains only zinc and copper. One such alloy weighing 15 gm ...
Given:
- The alloy contains only zinc and copper.
- The weight of the alloy is 15 gm.
- The ratio of zinc to copper in the alloy is 2:3 by weight.
- 10 gm of zinc is added to the alloy.
- The desired ratio of zinc to copper in the final alloy is 4:1 by weight.
To find:
The amount of copper that needs to be removed from the alloy to achieve the desired ratio.
Solution:
Step 1: Calculate the initial weights of zinc and copper in the alloy.
Let the weight of zinc in the alloy be x gm.
Then, the weight of copper in the alloy will be (15 - x) gm.
Given that the ratio of zinc to copper in the alloy is 2:3.
So, we can write the equation:
x / (15 - x) = 2 / 3
Step 2: Solve the equation to find the value of x.
Cross-multiplying the equation, we get:
3x = 2(15 - x)
3x = 30 - 2x
5x = 30
x = 6 gm
Therefore, the initial weight of zinc in the alloy is 6 gm and the weight of copper is (15 - 6) = 9 gm.
Step 3: Calculate the final weights of zinc and copper in the alloy.
After adding 10 gm of zinc to the alloy, the weight of zinc becomes (6 + 10) = 16 gm.
Let the weight of copper to be removed from the alloy be y gm.
Given that the desired ratio of zinc to copper in the final alloy is 4:1.
So, we can write the equation:
16 / (15 - y) = 4 / 1
Step 4: Solve the equation to find the value of y.
Cross-multiplying the equation, we get:
16 = 4(15 - y)
16 = 60 - 4y
4y = 60 - 16
4y = 44
y = 11 gm
Therefore, the amount of copper that needs to be removed from the alloy to achieve the desired ratio is 11 gm.
Hence, the correct answer is option A) 5 gm.