An alloy contains copper, zinc and nickel in the ratio of 5: 3: 2. The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5: 3:3 is

Options

A. 8
B. 10
C. 12
D. 15

Answer

To solve the problem, we need to determine how much nickel must be added to a 100 kg alloy that contains copper, zinc, and nickel in the ratio of 5:3:2, so that the new ratio becomes 5:3:3.

### Step-by-step Solution:

1. **Understand the Initial Ratio**:
The initial ratio of copper, zinc, and nickel is given as 5:3:2. This means that for every 10 parts of the alloy, 5 parts are copper, 3 parts are zinc, and 2 parts are nickel.

2. **Calculate the Total Parts**:
The total parts in the ratio is 5 + 3 + 2 = 10 parts.

3. **Determine the Weight of Each Component in the Alloy**:
Since the total weight of the alloy is 100 kg:
- Weight of copper = (5/10) * 100 kg = 50 kg
- Weight of zinc = (3/10) * 100 kg = 30 kg
- Weight of nickel = (2/10) * 100 kg = 20 kg

4. **Set Up the New Ratio**:
We want to change the ratio to 5:3:3. In this new ratio, the total parts are 5 + 3 + 3 = 11 parts.

5. **Calculate the New Weight of Nickel**:
In the new ratio, the weight of nickel should be:
- Weight of nickel = (3/11) * (100 kg + x), where x is the weight of nickel to be added.

6. **Set Up the Equation**:
We know the initial weight of nickel is 20 kg. Therefore, we can set up the equation:
\[ 20 + x = \frac{3}{11} \times (100 + x) \]

7. **Solve the Equation**:
Multiply both sides by 11 to eliminate the fraction:
\[ 11(20 + x) = 3(100 + x) \]
Expanding both sides:
\[ 220 + 11x = 300 + 3x \]
Rearranging gives:
\[ 11x - 3x = 300 - 220 \]
\[ 8x = 80 \]
Dividing both sides by 8:
\[ x = 10 \]

8. **Conclusion**:
The quantity of nickel that must be added to the alloy is **10 kg**.