The number of student passing or failing in an exam for a particular subject are presented in the bar chart below. Students who pass the exam cannot appear for the exam again. Students who fails the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt. The numbers of students who took the exam for the first time in the year 2nd the year 3 respectively, are ________.

The correct answer is 55 and 48.

Step-by-Step Explanation:

1. Understanding the Given Data from the Bar Chart:

From the provided bar chart, we can extract the number of students who passed and failed in each year:

• Year 1: Passed = 50, Failed = 10
• Year 2: Passed = 60, Failed = 5
• Year 3: Passed = 50, Failed = 3

2. Rules Given in the Question:

• Students who pass cannot take the exam again.
• Students who fail in their first attempt must take the exam again in the following year.
• Students always pass on their second attempt.

3. Calculating First-Time Exam Takers for Year 2:

In Year 1, 10 students failed their first attempt. Therefore, all these 10 students must reappear for the exam in Year 2 (as their second attempt) and pass.

Total students appearing for the exam in Year 2:

Out of these 65 students, 10 students are taking the exam for the second time (re-appearing from Year 1).

So, the number of students taking the exam for the first time in Year 2 is:

$\text{First-time takers in Year 2}=65-10=55$

4. Calculating First-Time Exam Takers for Year 3:

In Year 2, 5 students failed. Therefore, these 5 students must reappear for the exam in Year 3 (as their second attempt) and pass.

Total students appearing for the exam in Year 3:

$\text{Total students in Year 3}=\text{Passed}+\text{Failed}=50+3=53$

Out of these 53 students, 5 students are taking the exam for the second time (re-appearing from Year 2).

So, the number of students taking the exam for the first time in Year 3 is:

$\text{First-time takers in Year 3}=53-5=48$

Conclusion:

The number of students taking the exam for the first time in Year 2 and Year 3 respectively are 55 and 48.