Three sets of 40, 50 and 60 students appeared for an examination and the pass percentage was 100, 90 and 80 respectively. The pass percentage of the whole set is

Options

A. 88 `2/3` %
B. 84 `2/3` %
C. 88 `1/3` %
D. 84 `1/3` %

Answer

To find the overall pass percentage of the three sets of students, we will follow these steps:

### Step 1: Calculate the number of students who passed in each set.
- **Set 1:** 40 students with a pass percentage of 100%.
- Number of students who passed = 100% of 40 = \( 40 \times \frac{100}{100} = 40 \)

- **Set 2:** 50 students with a pass percentage of 90%.
- Number of students who passed = 90% of 50 = \( 50 \times \frac{90}{100} = 45 \)

- **Set 3:** 60 students with a pass percentage of 80%.
- Number of students who passed = 80% of 60 = \( 60 \times \frac{80}{100} = 48 \)

### Step 2: Calculate the total number of students who passed.
- Total students who passed = Students passed in Set 1 + Students passed in Set 2 + Students passed in Set 3
- Total students who passed = \( 40 + 45 + 48 = 133 \)

### Step 3: Calculate the total number of students who appeared for the examination.
- Total students = Students in Set 1 + Students in Set 2 + Students in Set 3
- Total students = \( 40 + 50 + 60 = 150 \)

### Step 4: Calculate the overall pass percentage.
- Overall pass percentage = \( \frac{\text{Total students who passed}}{\text{Total students}} \times 100 \)
- Overall pass percentage = \( \frac{133}{150} \times 100 \)

### Step 5: Simplify the fraction and calculate the percentage.
- First, simplify \( \frac{133}{150} \):
- \( \frac{133}{150} = 0.8867 \) (approximately)
- Now, multiply by 100 to get the percentage:
- Overall pass percentage = \( 0.8867 \times 100 \approx 88.67\% \)

### Final Answer:
The overall pass percentage of the whole set is approximately **88.67%**.

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