The weights of zinc and copper in an alloy are in the ratio `3:7.` If zinc weights `12.6 kg,` find the weight of the alloy.

Options

A. 40 kg
B. 42 kg
C. 39 kg
D. 38 kg

Answer

To solve the problem step by step, we will follow the given information and use the concept of ratios.

### Step 1: Understand the Ratio
The weights of zinc and copper in the alloy are in the ratio of 3:7. This means for every 3 parts of zinc, there are 7 parts of copper.

### Step 2: Define the Variables
Let:
- Weight of zinc = 3 parts
- Weight of copper = 7 parts

Given that the weight of zinc is 12.6 kg, we can denote the weight of copper as \( x \).

### Step 3: Set Up the Ratio Equation
From the ratio, we can write the equation:
\[ \frac{\text{Weight of Zinc}}{\text{Weight of Copper}} = \frac{3}{7} \]
Substituting the known weight of zinc:
\[ \frac{12.6}{x} = \frac{3}{7} \]

### Step 4: Cross Multiply
To solve for \( x \), we will cross multiply:
\[ 12.6 \times 7 = 3 \times x \]
This simplifies to:
\[ 88.2 = 3x \]

### Step 5: Solve for \( x \)
Now, divide both sides by 3 to find the weight of copper:
\[ x = \frac{88.2}{3} = 29.4 \text{ kg} \]

### Step 6: Calculate the Total Weight of the Alloy
The total weight of the alloy is the sum of the weights of zinc and copper:
\[ \text{Weight of Alloy} = \text{Weight of Zinc} + \text{Weight of Copper} \]
Substituting the values we have:
\[ \text{Weight of Alloy} = 12.6 + 29.4 = 42 \text{ kg} \]

### Final Answer
The weight of the alloy is **42 kg**.

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