X and Y are two alloys which are prepared by melting zinc and aluminum in the ratio of 1:4 and 11:8 respectively. If equal quantities of alloys are melted to form a third alloy Z what is the ratio of zinc and aluminum in alloy Z?

Options

A. `32:47`
B. `37:58`
C. `37:95`
D. `74:95`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Ratios of Alloys X and Y
Alloy X is made of zinc and aluminum in the ratio of 1:4. This means for every 1 part of zinc, there are 4 parts of aluminum.

Alloy Y is made of zinc and aluminum in the ratio of 11:8. This means for every 11 parts of zinc, there are 8 parts of aluminum.

### Step 2: Determine the Total Parts in Each Alloy
For Alloy X:
- Total parts = 1 (zinc) + 4 (aluminum) = 5 parts

For Alloy Y:
- Total parts = 11 (zinc) + 8 (aluminum) = 19 parts

### Step 3: Find a Common Quantity for Equal Mixing
Since we are melting equal quantities of both alloys, we can assume we take 1 unit of Alloy X and 1 unit of Alloy Y.

### Step 4: Calculate the Amount of Zinc and Aluminum in Each Alloy
For Alloy X (1 unit):
- Zinc = 1 part
- Aluminum = 4 parts

For Alloy Y (1 unit):
- Zinc = 11 parts
- Aluminum = 8 parts

### Step 5: Calculate Total Zinc and Aluminum in Alloy Z
When we combine both alloys:
- Total Zinc in Alloy Z = Zinc from Alloy X + Zinc from Alloy Y
= 1 + 11 = 12 parts

- Total Aluminum in Alloy Z = Aluminum from Alloy X + Aluminum from Alloy Y
= 4 + 8 = 12 parts

### Step 6: Determine the Ratio of Zinc to Aluminum in Alloy Z
The ratio of zinc to aluminum in Alloy Z is:
- Zinc : Aluminum = 12 : 12

### Step 7: Simplify the Ratio
This simplifies to:
- Zinc : Aluminum = 1 : 1

### Final Answer
The ratio of zinc to aluminum in alloy Z is **1:1**.

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