An alloy contains copper and tin in the ratio 3: 2. If 250 gm of copper is added to this alloy then the copper in it becomes double the quantity of tin in it. What is the amount in gma of tin in the alloy?

Options

A. 250
B. 750
C. 1000
D. 500

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Ratio
The alloy contains copper and tin in the ratio of 3:2. We can denote the amount of copper as \( C \) and the amount of tin as \( T \).

### Step 2: Express the Amounts in Terms of a Variable
Let’s denote the common multiplier for the ratio as \( x \). Therefore:
- Amount of copper, \( C = 3x \)
- Amount of tin, \( T = 2x \)

### Step 3: Add Copper to the Alloy
According to the problem, 250 grams of copper is added to the alloy. The new amount of copper becomes:
\[ C' = 3x + 250 \]

### Step 4: Set Up the Relationship After Adding Copper
After adding the copper, it is stated that the amount of copper becomes double the amount of tin. This can be expressed as:
\[ C' = 2T \]
Substituting the values we have:
\[ 3x + 250 = 2(2x) \]
This simplifies to:
\[ 3x + 250 = 4x \]

### Step 5: Solve for \( x \)
Now, we can rearrange the equation to solve for \( x \):
\[ 4x - 3x = 250 \]
\[ x = 250 \]

### Step 6: Find the Amount of Tin
Now that we have \( x \), we can find the amount of tin:
\[ T = 2x = 2(250) = 500 \text{ grams} \]

### Conclusion
The amount of tin in the alloy is **500 grams**.