Ratio of Copper to Zinc in New Alloy C
This problem involves calculating the final ratio of copper to zinc in a new alloy (Alloy C) formed by mixing equal amounts of two different alloys (Alloy A and Alloy B), each having a specific ratio of copper to zinc.
Understanding the Ratios
First, let's identify the composition of the initial alloys:
- Alloy A: Contains copper and zinc in the ratio 4:3. This means for every 4 parts of copper, there are 3 parts of zinc. The total number of parts in Alloy A is $4 + 3 = 7$.
- Alloy B: Contains copper and zinc in the ratio 9:5. This means for every 9 parts of copper, there are 5 parts of zinc. The total number of parts in Alloy B is $9 + 5 = 14$.
Mixing Equal Parts of Alloys
We are mixing equal parts of Alloy A and Alloy B to create Alloy C. To make the calculation straightforward, let's find a common basis for the parts. The total parts in Alloy A are 7, and in Alloy B are 14. The least common multiple (LCM) of 7 and 14 is 14.
Let's assume we take 14 units of Alloy A and 14 units of Alloy B. This ensures we are mixing equal quantities.
Composition of Alloy A (14 units)
- Amount of Copper in 14 units of Alloy A = $ \frac{4}{7} \times 14 \text{ units} = 8 \text{ units} $
- Amount of Zinc in 14 units of Alloy A = $ \frac{3}{7} \times 14 \text{ units} = 6 \text{ units} $
Composition of Alloy B (14 units)
- Amount of Copper in 14 units of Alloy B = $ \frac{9}{14} \times 14 \text{ units} = 9 \text{ units} $
- Amount of Zinc in 14 units of Alloy B = $ \frac{5}{14} \times 14 \text{ units} = 5 \text{ units} $
Calculating the Ratio in Alloy C
Now, we mix these amounts to form the new Alloy C:
- Total Copper in Alloy C: Sum of copper from Alloy A and Alloy B. $ \text{Total Copper} = 8 \text{ units} + 9 \text{ units} = 17 \text{ units} $
- Total Zinc in Alloy C: Sum of zinc from Alloy A and Alloy B. $ \text{Total Zinc} = 6 \text{ units} + 5 \text{ units} = 11 \text{ units} $
Therefore, the ratio of copper to zinc in the new Alloy C is the ratio of the total copper to the total zinc:
$ \text{Ratio in Alloy C} = \text{Total Copper} : \text{Total Zinc} = 17:11 $Important Questions from To Make a Mixture from Two Mixtures
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