2500 students appeared in an examination in which `(1)/(5)` of the total students are girls and remaining are boys 15% boys and 40% girls are failed. What is the percentage of passed students.

Options

A. 85
B. 86
C. 88
D. 80

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Calculate the number of girls and boys.
Given that \( \frac{1}{5} \) of the total students are girls, we can find the number of girls:

\[ \text{Number of girls} = \frac{1}{5} \times 2500 = 500 \]

Now, to find the number of boys, we subtract the number of girls from the total number of students:

\[ \text{Number of boys} = 2500 - 500 = 2000 \]

### Step 2: Calculate the number of failed boys.
We know that 15% of the boys failed. To find the number of failed boys:

\[ \text{Failed boys} = 15\% \text{ of } 2000 = \frac{15}{100} \times 2000 = 300 \]

### Step 3: Calculate the number of passed boys.
To find the number of boys who passed, we subtract the number of failed boys from the total number of boys:

\[ \text{Passed boys} = 2000 - 300 = 1700 \]

### Step 4: Calculate the number of failed girls.
Next, we know that 40% of the girls failed. To find the number of failed girls:

\[ \text{Failed girls} = 40\% \text{ of } 500 = \frac{40}{100} \times 500 = 200 \]

### Step 5: Calculate the number of passed girls.
To find the number of girls who passed, we subtract the number of failed girls from the total number of girls:

\[ \text{Passed girls} = 500 - 200 = 300 \]

### Step 6: Calculate the total number of passed students.
Now, we can find the total number of students who passed by adding the number of passed boys and passed girls:

\[ \text{Total passed students} = 1700 + 300 = 2000 \]

### Step 7: Calculate the percentage of passed students.
Finally, to find the percentage of students who passed, we use the formula:

\[ \text{Percentage of passed students} = \left( \frac{\text{Total passed students}}{\text{Total students}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage of passed students} = \left( \frac{2000}{2500} \right) \times 100 = 80\% \]

### Final Answer:
The percentage of passed students is **80%**.

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