In an alloy A, Aluminum and Nickel are present in the ratio 4:3 respectively and in alloy B, the same element are in the ratio 3:5 respectively. If these two alloys be mixed to form a new alloy in which same elements are in the ratio 1:1 respectively, then find the ratio of alloy A and alloy B in the new alloy?

Options

A. `6:7`
B. `7:4`
C. `4:7`
D. `7:6`

Answer

To solve the problem step by step, we will analyze the given information about the two alloys and set up equations based on the ratios provided.

### Step-by-Step Solution:

1. **Understand the Ratios in Alloys:**
- In Alloy A, Aluminum and Nickel are in the ratio of 4:3.
- In Alloy B, Aluminum and Nickel are in the ratio of 3:5.

2. **Assume Quantities of Alloys:**
- Let the quantity of Alloy A be \( x \) and the quantity of Alloy B be \( y \).

3. **Calculate Aluminum and Nickel in Alloy A:**
- Total parts in Alloy A = \( 4 + 3 = 7 \).
- Aluminum in Alloy A = \( \frac{4}{7}x \).
- Nickel in Alloy A = \( \frac{3}{7}x \).

4. **Calculate Aluminum and Nickel in Alloy B:**
- Total parts in Alloy B = \( 3 + 5 = 8 \).
- Aluminum in Alloy B = \( \frac{3}{8}y \).
- Nickel in Alloy B = \( \frac{5}{8}y \).

5. **Set Up the Equation for the New Alloy:**
- When Alloy A and Alloy B are mixed, the total Aluminum and Nickel in the new alloy should be in the ratio of 1:1.
- Therefore, we can write the equation:
\[ \frac{\frac{4}{7}x + \frac{3}{8}y}{\frac{3}{7}x + \frac{5}{8}y} = 1 \]

6. **Cross-Multiply to Eliminate the Fraction:**
- This gives us:
\[ \frac{4}{7}x + \frac{3}{8}y = \frac{3}{7}x + \frac{5}{8}y \]

7. **Rearranging the Equation:**
- Move all terms involving \( x \) to one side and \( y \) to the other side:
\[ \frac{4}{7}x - \frac{3}{7}x = \frac{5}{8}y - \frac{3}{8}y \]
- Simplifying gives:
\[ \frac{1}{7}x = \frac{2}{8}y \]
- This simplifies to:
\[ \frac{1}{7}x = \frac{1}{4}y \]

8. **Cross-Multiply Again:**
- Cross-multiplying gives:
\[ 4x = 7y \]

9. **Find the Ratio of Alloy A to Alloy B:**
- Rearranging gives:
\[ \frac{x}{y} = \frac{7}{4} \]
- Therefore, the ratio of Alloy A to Alloy B is:
\[ x:y = 7:4 \]

### Final Answer:
The ratio of Alloy A to Alloy B in the new alloy is **7:4**.