An alloy 'A' made of Copper and Zinc contain 40% copper and another alloy 'B' having same elements contain 30% zinc. A new alloy is made by mixing both alloys which contain 60% copper. Find the ratio of quantity of alloy A and alloy B in the new alloy?

Options

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

Answer

To solve the problem of finding the ratio of quantities of alloy A and alloy B in the new alloy, we can follow these steps:

### Step 1: Understand the Composition of Alloys
- Alloy A contains 40% copper and 60% zinc.
- Alloy B contains 30% zinc, which means it contains 70% copper (since copper and zinc are the only components).

### Step 2: Define the Percentages
- For Alloy A:
- Copper = 40%
- Zinc = 60%

- For Alloy B:
- Copper = 70%
- Zinc = 30%

### Step 3: Determine the Composition of the New Alloy
- The new alloy contains 60% copper. Therefore, it contains 40% zinc.

### Step 4: Set Up the Allegation Method
We will use the allegation method to find the ratio of the two alloys.

1. **Write down the percentages of copper in each alloy and the new alloy:**
- Alloy A: 40% copper
- Alloy B: 70% copper
- New Alloy: 60% copper

2. **Set up the allegation:**
- The difference between Alloy A and the new alloy:
\[ 60\% - 40\% = 20\% \]
- The difference between Alloy B and the new alloy:
\[ 70\% - 60\% = 10\% \]

### Step 5: Calculate the Ratio
- The ratio of the quantities of Alloy A to Alloy B is given by the differences calculated:
\[ \text{Ratio of Alloy A to Alloy B} = \frac{10}{20} = \frac{1}{2} \]

### Conclusion
The ratio of the quantity of alloy A to alloy B in the new alloy is **1:2**.

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