In a school, `60%` of the numberof students are boys and the rest are girls. If `20%` of the number of boys failed and `65%` of the number of girls passed the examination, then the percentage of the total number of students who passed is:

Options

A. a)68
B. b)72
C. c)74
D. d)78

Answer

To solve the problem, let's break it down step by step.

### Step 1: Determine the number of boys and girls
Let the total number of students in the school be 100 (this makes calculations easier).

- Number of boys = 60% of 100 = 60 boys
- Number of girls = 40% of 100 = 40 girls

### Step 2: Calculate the number of boys who passed
According to the problem, 20% of the boys failed the examination.

- Number of boys who failed = 20% of 60 = 0.20 * 60 = 12 boys
- Therefore, the number of boys who passed = Total boys - Boys who failed = 60 - 12 = 48 boys

### Step 3: Calculate the number of girls who passed
According to the problem, 65% of the girls passed the examination.

- Number of girls who passed = 65% of 40 = 0.65 * 40 = 26 girls

### Step 4: Calculate the total number of students who passed
Now, we can find the total number of students who passed the examination.

- Total passed = Boys who passed + Girls who passed = 48 + 26 = 74 students

### Step 5: Calculate the percentage of total students who passed
Finally, we need to find the percentage of the total number of students who passed.

- Percentage of students who passed = (Total passed / Total students) * 100
- Percentage of students who passed = (74 / 100) * 100 = 74%

### Final Answer:
The percentage of the total number of students who passed is **74%**.

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