In an alloy, aluminium and tin are in the ratio of 4:5. In the second alloy, the ratio of same elements is 4:7. If equal quantities of these two alloys be mixed to form a new alloy, then what will be the ratio of both of these elements in the new alloy?

Options

A. `2:3`
B. `16:35`
C. `4:5`
D. `40:59`

Answer

To solve the problem, we need to find the ratio of aluminium and tin in the new alloy formed by mixing equal quantities of two alloys. Let's break down the solution step by step.

### Step 1: Understand the Ratios in Each Alloy
- In the first alloy, the ratio of aluminium to tin is 4:5.
- In the second alloy, the ratio of aluminium to tin is 4:7.

### Step 2: Determine the Total Parts in Each Alloy
- For the first alloy:
- Total parts = 4 (aluminium) + 5 (tin) = 9 parts.

- For the second alloy:
- Total parts = 4 (aluminium) + 7 (tin) = 11 parts.

### Step 3: Assume Equal Quantities of Each Alloy
Let’s assume we take 9 units of the first alloy and 11 units of the second alloy to maintain equal quantities for the calculation.

### Step 4: Calculate the Amount of Aluminium and Tin in Each Alloy
- **For Alloy 1 (9 units total)**:
- Aluminium = (4/9) * 9 = 4 units
- Tin = (5/9) * 9 = 5 units

- **For Alloy 2 (11 units total)**:
- Aluminium = (4/11) * 11 = 4 units
- Tin = (7/11) * 11 = 7 units

### Step 5: Combine the Quantities of Aluminium and Tin
Now, we combine the amounts of aluminium and tin from both alloys:
- Total Aluminium = 4 (from Alloy 1) + 4 (from Alloy 2) = 8 units
- Total Tin = 5 (from Alloy 1) + 7 (from Alloy 2) = 12 units

### Step 6: Find the Ratio of Aluminium to Tin in the New Alloy
Now, we can find the ratio of aluminium to tin in the new alloy:
- Ratio = Total Aluminium : Total Tin = 8 : 12

### Step 7: Simplify the Ratio
To simplify the ratio:
- Divide both sides by their greatest common divisor (GCD), which is 4:
- 8 ÷ 4 = 2
- 12 ÷ 4 = 3
- Therefore, the simplified ratio is 2 : 3.

### Final Answer
The ratio of aluminium to tin in the new alloy is **2 : 3**.

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