In a shipment of 120 machine parts, 5 per cent were defective. In a shipment of 80 machine parts, 10 per cent were defective. For the two shipments combined, what per cent of the machine parts were defective? 

Options

A. `6.5%`
B. `7.0%`
C. `7.5%`
D. `8.0%`

Answer

To find the percentage of defective machine parts in the combined shipments, we can follow these steps:

### Step 1: Calculate the number of defective parts in the first shipment.
- The first shipment has 120 machine parts, and 5% of them are defective.
- To find the number of defective parts, use the formula:
\[ \text{Defective parts} = \frac{\text{Percentage}}{100} \times \text{Total parts} \]
- Substituting the values:
\[ \text{Defective parts} = \frac{5}{100} \times 120 = 6 \]

### Step 2: Calculate the number of defective parts in the second shipment.
- The second shipment has 80 machine parts, and 10% of them are defective.
- Again, using the same formula:
\[ \text{Defective parts} = \frac{10}{100} \times 80 = 8 \]

### Step 3: Calculate the total number of defective parts from both shipments.
- Add the defective parts from both shipments:
\[ \text{Total defective parts} = 6 + 8 = 14 \]

### Step 4: Calculate the total number of machine parts in both shipments.
- The total number of machine parts is:
\[ \text{Total parts} = 120 + 80 = 200 \]

### Step 5: Calculate the percentage of defective parts in the combined shipments.
- Use the formula for percentage:
\[ \text{Percentage of defective parts} = \left(\frac{\text{Total defective parts}}{\text{Total parts}}\right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of defective parts} = \left(\frac{14}{200}\right) \times 100 = 7\% \]

### Final Answer:
The percentage of defective machine parts in the combined shipments is **7%**.

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