60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, then the amount of tin in the new alloy is

Options

A. 36 kg
B. 44 kg
C. 53 kg
D. 80 kg

Answer

To solve the problem, we need to find the amount of tin in the new alloy formed by mixing alloy A and alloy B. Let's break it down step by step.

### Step 1: Determine the composition of Alloy A
Alloy A has lead and tin in the ratio of 3:2. This means that for every 5 parts of the alloy, 3 parts are lead and 2 parts are tin.

- Total parts in Alloy A = 3 + 2 = 5
- Weight of Alloy A = 60 kg

Now, we can calculate the amount of tin in Alloy A:

\[ \text{Amount of tin in Alloy A} = \left(\frac{2}{5}\right) \times 60 \text{ kg} \]

Calculating this gives:

\[ \text{Amount of tin in Alloy A} = \frac{120}{5} = 24 \text{ kg} \]

### Step 2: Determine the composition of Alloy B
Alloy B has tin and copper in the ratio of 1:4. This means that for every 5 parts of the alloy, 1 part is tin and 4 parts are copper.

- Total parts in Alloy B = 1 + 4 = 5
- Weight of Alloy B = 100 kg

Now, we can calculate the amount of tin in Alloy B:

\[ \text{Amount of tin in Alloy B} = \left(\frac{1}{5}\right) \times 100 \text{ kg} \]

Calculating this gives:

\[ \text{Amount of tin in Alloy B} = \frac{100}{5} = 20 \text{ kg} \]

### Step 3: Calculate the total amount of tin in the new alloy
Now that we have the amount of tin from both alloys, we can find the total amount of tin in the new alloy:

\[ \text{Total amount of tin} = \text{Amount of tin in Alloy A} + \text{Amount of tin in Alloy B} \]

Substituting the values we calculated:

\[ \text{Total amount of tin} = 24 \text{ kg} + 20 \text{ kg} = 44 \text{ kg} \]

### Final Answer
The total amount of tin in the new alloy is **44 kg**.

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