A and B are the alloys of Lead and Iron in the ratio of 4 : 3 and 2 : 5 respectively. Another alloy C is formed by mixing A and B in the ratio of 3 : 4. Find the final ratio of Lead and Iron in C.

To solve this problem, we need to determine the ratio of Lead to Iron in alloy C, which is formed by mixing alloys A and B in the given ratio. Let's break it down step by step.

### Step 1: Determine the composition of alloys A and B.
- **Alloy A** has Lead and Iron in the ratio \(4 : 3\). 
- **Alloy B** has Lead and Iron in the ratio \(2 : 5\).

### Step 2: Assume quantities of alloys A and B.
Let the quantity of Alloy A be \(3x\) and the quantity of Alloy B be \(4x\), since they are mixed in the ratio \(3 : 4\).

### Step 3: Calculate the amount of Lead and Iron in A and B.
- In **Alloy A**:
  - Amount of Lead in A = \(3x \times \frac{4}{7} = \frac{12x}{7}\)
  - Amount of Iron in A = \(3x \times \frac{3}{7} = \frac{9x}{7}\)

- In **Alloy B**:
  - Amount of Lead in B = \(4x \times \frac{2}{7} = \frac{8x}{7}\)
  - Amount of Iron in B = \(4x \times \frac{5}{7} = \frac{20x}{7}\)

### Step 4: Add the amounts from A and B to get the total Lead and Iron in C.
- Total Lead in C = \(\frac{12x}{7} + \frac{8x}{7} = \frac{20x}{7}\)
- Total Iron in C = \(\frac{9x}{7} + \frac{20x}{7} = \frac{29x}{7}\)

### Step 5: Find the ratio of Lead to Iron in alloy C.
- Ratio of Lead to Iron in C = \(\frac{20x/7}{29x/7} = \frac{20}{29}\)

### Final Answer:
The final ratio of Lead to Iron in alloy C is **20 : 29**.

Would you like further details or have any other questions? 

Here are five related questions:
1. How would the ratio change if the mixing ratio of A and B were different?
2. What is the total amount of Lead in alloy C if \(x = 7\) units?
3. How would you calculate the ratio if one of the alloys had an additional metal?
4. What would happen to the ratio if the proportion of Lead in alloy A were increased?
5. Can this method be applied to find the ratio of other elements in different alloys?

**Tip:** When dealing with mixtures or alloys, always break down the problem by calculating the individual contributions of each component before combining them.

Discover how to find the final ratio of Lead and Iron in alloy C using mixtures and solutions concepts. This problem involves determining the composition of alloys A and B and mixing them in a specific ratio to form alloy C. Learn step-by-step with detailed calculations and ratios. Suitable for Grades 7-9.

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