An alloy contains zinc, copper and tin in the ratio 2:3:1 and another contains copper, tin and lead in the ratio 5:4:3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in the new alloy will be

Options

A. `(1)/(2)` kg
B. `(1)/(8)` kg
C. `(3)/(14)` kg
D. `(7)/(9)` kg

Answer

To solve the problem, we need to determine the weight of lead per kg in the new alloy formed by melting equal weights of two different alloys. Let's break down the solution step by step.

### Step 1: Understand the Ratios of the Alloys
The first alloy contains zinc, copper, and tin in the ratio of 2:3:1. This means:
- Zinc = 2 parts
- Copper = 3 parts
- Tin = 1 part

The total parts in the first alloy = 2 + 3 + 1 = 6 parts.

The second alloy contains copper, tin, and lead in the ratio of 5:4:3. This means:
- Copper = 5 parts
- Tin = 4 parts
- Lead = 3 parts

The total parts in the second alloy = 5 + 4 + 3 = 12 parts.

### Step 2: Determine the Weight of Each Metal in a Common Weight
Assume we take 12 kg of each alloy for easier calculations (the LCM of 6 and 12 is 12).

For the first alloy (12 kg):
- Zinc = (2/6) * 12 = 4 kg
- Copper = (3/6) * 12 = 6 kg
- Tin = (1/6) * 12 = 2 kg

For the second alloy (12 kg):
- Copper = (5/12) * 12 = 5 kg
- Tin = (4/12) * 12 = 4 kg
- Lead = (3/12) * 12 = 3 kg

### Step 3: Combine the Weights of Each Metal
Now, we combine the weights of each metal from both alloys:
- Zinc = 4 kg (from the first alloy)
- Copper = 6 kg (from the first alloy) + 5 kg (from the second alloy) = 11 kg
- Tin = 2 kg (from the first alloy) + 4 kg (from the second alloy) = 6 kg
- Lead = 3 kg (from the second alloy)

### Step 4: Total Weight of the New Alloy
Now, let's find the total weight of the new alloy:
Total weight = Zinc + Copper + Tin + Lead
= 4 kg + 11 kg + 6 kg + 3 kg = 24 kg

### Step 5: Calculate the Weight of Lead per kg in the New Alloy
To find the weight of lead per kg in the new alloy, we divide the weight of lead by the total weight of the new alloy:
Weight of lead per kg = Weight of lead / Total weight of new alloy
= 3 kg / 24 kg = 1/8 kg

### Final Answer
The weight of lead per kg in the new alloy is **1/8 kg**.

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