Question

The number of students passing or failing in an exam are shown in the bar chart. Students who pass do not appear again. Students who fail must reappear the next year and always pass in their second attempt. Find the number of students who took the exam for the first time in Year 2 and Year 3. 

 

• A. 65 and 53
• B. 60 and 50
• C. 55 and 53
• D. 55 and 48

Hint:

Always subtract repeaters (previous year fails) from the total strength to find new candidates.

Answer 1

The Correct Option is D

Step 1: Use Year 1 data.
Year 1: Pass = 50, Fail = 10.
Thus 10 failed students must appear again in Year 2.

Step 2: Use Year 2 totals.
Year 2: Pass = 60, Fail = 5 → total = 65.
Since 10 are repeaters: \[ \text{New students in Year 2} = 65 - 10 = 55. \]

Step 3: Use Year 3 data.
Year 2 failures = 5 → these 5 must appear again in Year 3.
Year 3: Pass = 50, Fail = 3 → total = 53.
Thus new students in Year 3: \[ 53 - 5 = 48. \]

Step 4: Final result.
Number of first-time candidates: Year 2 → 55 Year 3 → 48