In the half-yearly exam, 60% of students passed. Out of these students, 70% passed the annual exam. Out of the remaining students (who failed the half-yearly exam), 80% passed the annual exam. What percentage of the students passed the annual exam?
Let's assume the total number of students is 100 for easy calculation.
Step 1: Students Who Passed the Half-Yearly Exam
60% of students passed the half-yearly exam.
So, the number of students who passed the half-yearly exam =
\[
\frac{60}{100} \times 100 = 60
\]
40% failed the half-yearly exam.
So, the number of students who failed the half-yearly exam =
\[
\frac{40}{100} \times 100 = 40
\]
Step 2: Students Who Passed the Annual Exam
70% of students who passed the half-yearly exam passed the annual exam:
\[
\frac{70}{100} \times 60 = 42
\]
80% of students who failed the half-yearly exam passed the annual exam:
\[
\frac{80}{100} \times 40 = 32
\]
Step 3: Total Students Who Passed the Annual Exam
\[
42 + 32 = 74
\]
Step 4: Percentage of Students Who Passed the Annual Exam
Since the total number of students was 100, the percentage of students who passed the annual exam is:
\[
\frac{74}{100} \times 100 = 74\%
\]
Final Answer
\( 74\%
\)
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