Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?

Options

A. 58 kg
B. 60 kg
C. 64 kg
D. 70 kg

Answer

To solve the problem step by step, we will follow the given information about the ratio of zinc and copper and the amount of zinc used.

### Step 1: Understand the Ratio
The problem states that zinc and copper are melted together in the ratio of 9:11. This means for every 9 parts of zinc, there are 11 parts of copper.

### Step 2: Define Variables
Let the common multiple be represented by \( K \). Therefore, the amount of zinc can be expressed as:
- Zinc = \( 9K \) kg
- Copper = \( 11K \) kg

### Step 3: Total Weight of the Mixture
The total weight of the melted mixture can be calculated as:
\[ \text{Total Weight} = \text{Weight of Zinc} + \text{Weight of Copper} = 9K + 11K = 20K \text{ kg} \]

### Step 4: Find the Value of \( K \)
We know from the problem that 28.8 kg of zinc has been consumed. Therefore, we can set up the equation:
\[ 9K = 28.8 \text{ kg} \]
To find \( K \), we divide both sides by 9:
\[ K = \frac{28.8}{9} \]

### Step 5: Calculate \( K \)
Calculating the value of \( K \):
\[ K = \frac{28.8}{9} = 3.2 \text{ kg} \]

### Step 6: Calculate the Total Weight of the Mixture
Now that we have the value of \( K \), we can find the total weight of the melted mixture:
\[ \text{Total Weight} = 20K = 20 \times 3.2 \]
Calculating this gives:
\[ \text{Total Weight} = 64 \text{ kg} \]

### Conclusion
The weight of the melted mixture is **64 kg**.

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