Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are `5 : 3` and `1 : 2`, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio `4 : 3`. What is the ratio of the composition of the two basic elements in alloy X ?

Options

A. `1 : 1`
B. `2 : 3`
C. `5 : 2`
D. `4 : 3`

Answer

To find the ratio of the composition of the two basic elements in alloy X formed by mixing alloys A and B, we can follow these steps:

### Step 1: Determine the compositions of alloys A and B
- For alloy A, the ratio of the two basic elements is 5:3.
- Let the total parts = 5 + 3 = 8.
- The fraction of the first basic element in alloy A = 5/8.
- The fraction of the second basic element in alloy A = 3/8.

- For alloy B, the ratio of the two basic elements is 1:2.
- Let the total parts = 1 + 2 = 3.
- The fraction of the first basic element in alloy B = 1/3.
- The fraction of the second basic element in alloy B = 2/3.

### Step 2: Mix alloys A and B in the ratio 4:3
- Let the quantity of alloy A be 4Y and the quantity of alloy B be 3Y.

### Step 3: Calculate the amount of the first basic element in alloy X
- Amount of the first basic element from alloy A:
\[ \text{Amount from A} = \left(\frac{5}{8}\right) \times 4Y = \frac{20Y}{8} = \frac{5Y}{2} \]

- Amount of the first basic element from alloy B:
\[ \text{Amount from B} = \left(\frac{1}{3}\right) \times 3Y = 1Y \]

- Total amount of the first basic element in alloy X:
\[ \text{Total} = \frac{5Y}{2} + 1Y = \frac{5Y}{2} + \frac{2Y}{2} = \frac{7Y}{2} \]

### Step 4: Calculate the amount of the second basic element in alloy X
- Amount of the second basic element from alloy A:
\[ \text{Amount from A} = \left(\frac{3}{8}\right) \times 4Y = \frac{12Y}{8} = \frac{3Y}{2} \]

- Amount of the second basic element from alloy B:
\[ \text{Amount from B} = \left(\frac{2}{3}\right) \times 3Y = 2Y \]

- Total amount of the second basic element in alloy X:
\[ \text{Total} = \frac{3Y}{2} + 2Y = \frac{3Y}{2} + \frac{4Y}{2} = \frac{7Y}{2} \]

### Step 5: Find the ratio of the two basic elements in alloy X
- The ratio of the first basic element to the second basic element in alloy X is:
\[ \text{Ratio} = \frac{\frac{7Y}{2}}{\frac{7Y}{2}} = 1:1 \]

### Final Answer
The ratio of the composition of the two basic elements in alloy X is **1:1**.

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