Let's denote the total number of candidates listed for the exam as \( T \).
Given information:
1. 5% of all candidates are absent.
2. 80% of the appeared candidates passed.
Now, let's calculate the number of candidates who appeared for the exam. The number of absent candidates is \( 0.05 \times T \), and the number of candidates who appeared is \( T - 0.05 \times T \).
The percentage of candidates who passed among those who appeared is \( 80\% \).
Now, let's find the total number of candidates who passed:
\[ \text{Total candidates passed} = 0.80 \times (T - 0.05 \times T) \]
To find the percentage of all listed candidates who passed, we need to express this as a percentage of the total listed candidates:
\[ \text{Percentage of candidates passed} = \left( \frac{\text{Total candidates passed}}{T} \right) \times 100 \]
Substitute the expression for total candidates passed:
\[ \text{Percentage of candidates passed} = \left( \frac{0.80 \times (T - 0.05 \times T)}{T} \right) \times 100 \]
Simplify the expression:
\[ \text{Percentage of candidates passed} = \left( \frac{0.80 \times (0.95 \times T)}{T} \right) \times 100 \]
Simplify further:
\[ \text{Percentage of candidates passed} = 0.76 \times 100 \]
\[ \text{Percentage of candidates passed} = 76\% \]
So, 76% of all the listed candidates passed the exam.
Given information:
1. 5% of all candidates are absent.
2. 80% of the appeared candidates passed.
Now, let's calculate the number of candidates who appeared for the exam. The number of absent candidates is \( 0.05 \times T \), and the number of candidates who appeared is \( T - 0.05 \times T \).
The percentage of candidates who passed among those who appeared is \( 80\% \).
Now, let's find the total number of candidates who passed:
\[ \text{Total candidates passed} = 0.80 \times (T - 0.05 \times T) \]
To find the percentage of all listed candidates who passed, we need to express this as a percentage of the total listed candidates:
\[ \text{Percentage of candidates passed} = \left( \frac{\text{Total candidates passed}}{T} \right) \times 100 \]
Substitute the expression for total candidates passed:
\[ \text{Percentage of candidates passed} = \left( \frac{0.80 \times (T - 0.05 \times T)}{T} \right) \times 100 \]
Simplify the expression:
\[ \text{Percentage of candidates passed} = \left( \frac{0.80 \times (0.95 \times T)}{T} \right) \times 100 \]
Simplify further:
\[ \text{Percentage of candidates passed} = 0.76 \times 100 \]
\[ \text{Percentage of candidates passed} = 76\% \]
So, 76% of all the listed candidates passed the exam.