A motor has 120 machine parts of which 5% are defective. Another motor has 80 machine parts of which 10% are defective. Considering both motors together, what is the overall percentage of defective machine parts?

Introduction / Context:
This question is about combined percentages over two different groups. Each motor has its own percentage of defective parts and a specific number of parts. To find the overall percentage of defective parts when the two motors are considered together, we must work with actual numbers of defective parts rather than averaging the percentages directly. This concept is important in quality control and data analysis problems where different batches or groups are combined.

Given Data / Assumptions:

• Motor 1 has 120 machine parts and 5% of them are defective.
• Motor 2 has 80 machine parts and 10% of them are defective.
• We assume each percentage is calculated correctly for its own motor.
• We need the overall percentage of defective parts across both motors combined.

Concept / Approach:
The correct method is to find the total number of defective parts in each motor, sum them, and divide by the total number of parts from both motors. Then we convert that fraction into a percentage. Averaging the two percentages directly (for example, (5% + 10%) / 2) would be wrong because the motors have different total numbers of parts, so their contributions are not equal.

Step-by-Step Solution:
Step 1: For motor 1, total parts = 120. Defective percentage = 5%. Step 2: Defective parts in motor 1 = 5% of 120 = 120 * 5/100 = 6. Step 3: For motor 2, total parts = 80. Defective percentage = 10%. Step 4: Defective parts in motor 2 = 10% of 80 = 80 * 10/100 = 8. Step 5: Total defective parts in both motors = 6 + 8 = 14. Step 6: Total machine parts in both motors = 120 + 80 = 200. Step 7: Overall defective percentage = (14 / 200) * 100 = 7%.

Verification / Alternative check:
Another way to sanity check is to note that the combined group has 200 parts and 14 defective parts. Since 10% of 200 would be 20, and we have 14 defective parts, the overall defective percentage must be less than 10%. Likewise, 5% of 200 would be 10, and 14 is slightly above that, so the percentage should be slightly above 5%. The computed value 7% fits comfortably in this range and is reasonable.

Why Other Options Are Wrong:

• 6.5 and 7.5 are close but do not match the exact calculation from 14/200.
• 8% would correspond to 16 defective parts out of 200, which is more than the actual count of 14.

Common Pitfalls:
A typical mistake is to average the percentages as (5 + 10)/2 = 7.5 without considering different quantities in each group. This gives a value close to the correct answer but still wrong. Another error is miscalculating the defective parts by applying percentages incorrectly to 120 or 80. Finally, some learners forget to convert the fraction into a percentage by multiplying by 100. Precise stepwise calculation helps avoid these problems.

Final Answer:
The overall percentage of defective machine parts is 7%.