Gold is 12 times as heavy as aluminum and copper is 5 times as heavy as aluminum.In what ratio gold and copper should be mixed to get an alloy 8 times of aluminum.

Options

A. 2 : 1
B. 3 : 4
C. 1 : 2
D. 4 : 3

Answer

To solve the problem of finding the ratio in which gold and copper should be mixed to obtain an alloy that is 8 times as heavy as aluminum, we can use the method of allegation. Here is the step-by-step solution:

### Step 1: Define the weights of the metals in relation to aluminum
- Let the weight of aluminum be represented as 1 unit.
- Since gold is 12 times as heavy as aluminum, the weight of gold is \(12 \times 1 = 12\) units.
- Since copper is 5 times as heavy as aluminum, the weight of copper is \(5 \times 1 = 5\) units.

### Step 2: Define the weight of the desired alloy
- The desired alloy is 8 times as heavy as aluminum, which means its weight is \(8 \times 1 = 8\) units.

### Step 3: Set up the allegation
- We will use the weights we defined:
- Weight of gold = 12 units
- Weight of copper = 5 units
- Weight of the desired alloy = 8 units

### Step 4: Calculate the differences
- Calculate the difference between the weight of gold and the desired alloy:
\[ 12 - 8 = 4 \]
- Calculate the difference between the weight of copper and the desired alloy:
\[ 8 - 5 = 3 \]

### Step 5: Form the ratio
- The ratio of gold to copper can be represented as the inverse of the differences calculated:
\[ \text{Ratio of gold to copper} = \frac{3}{4} \]

### Conclusion
- Therefore, gold and copper should be mixed in the ratio of \(3:4\).