In the half yearly exam, only 60% of the students were passed. Out of these (passed in half-yearly), only 70% students are passed in annual exam. Out of remaining students (who fail in half-yearly exam) 80% passed in annual exam. What percent of the students passed the annual exam?
Show Hint
- 76%
- 72%
- 74%
- 65%
The Correct Option is C
Solution and Explanation
Step 1: Define the total number of students.
Let the total number of students be \( x \).
Step 2: Find the number of students passing in the half-yearly exam.
- 60% of \( x \) passed in the half-yearly exam, so:
\[
\text{Number of students passing half-yearly} = 0.60x.
\]
- 70% of these \( 0.60x \) passed the annual exam, so:
\[
\text{Number of students passing annual exam (half-yearly pass)} = 0.70 \times 0.60x = 0.42x.
\]
Step 3: Find the number of students failing in the half-yearly exam.
- 40% of \( x \) failed in the half-yearly exam, so:
\[
\text{Number of students failing half-yearly} = 0.40x.
\]
- 80% of these \( 0.40x \) passed the annual exam, so:
\[
\text{Number of students passing annual exam (half-yearly fail)} = 0.80 \times 0.40x = 0.32x.
\]
Step 4: Calculate the total number of students passing the annual exam.
The total number of students passing the annual exam is the sum of those who passed the annual exam from both groups:
\[
\text{Total passing the annual exam} = 0.42x + 0.32x = 0.74x.
\]
Step 5: Calculate the percentage.
The percentage of students passing the annual exam is:
\[
\text{Percentage passing annual exam} = \frac{0.74x}{x} \times 100 = 74%.
\]
Step 6: Conclusion.
Thus, 74% of the students passed the annual exam, and the correct answer is (c).
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