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The number of students passing or failing in an exam for a particular subject is presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail 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 number of students who took the exam for the first time in the year $2$ and the year $3$ respectively, are ______________.

- $65$ and $53$
- $60$ and $50$
- $55$ and $53$
- $55$ and $48$

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Best answer

The total number of students in $\text{Year 2} = 60 \text{(pass)} + 5 \text{(fail)} = 65$

The number of students, who failed in the exam in $\text{Year 1}$, and appeared in $\text{Year 2} = 10$

$\therefore$ The total number of students in $\text{Year 2}$ who appeared for the first time $ = 65 – 10 = 55$

Similarly, the total number of students in $\text{Year 3} = 50 \text{(pass)} + 3 \text{(fail)} = 53$

The number of students, who failed in the exam in $\text{Year 2}$, and appeared in $\text{Year 3} = 5$

$\therefore$ The total number of students in $\text{Year 3}$ who appeared for the first time $ = 53-5 = 48$

So, the correct answer is $(D).$

The number of students, who failed in the exam in $\text{Year 1}$, and appeared in $\text{Year 2} = 10$

$\therefore$ The total number of students in $\text{Year 2}$ who appeared for the first time $ = 65 – 10 = 55$

Similarly, the total number of students in $\text{Year 3} = 50 \text{(pass)} + 3 \text{(fail)} = 53$

The number of students, who failed in the exam in $\text{Year 2}$, and appeared in $\text{Year 3} = 5$

$\therefore$ The total number of students in $\text{Year 3}$ who appeared for the first time $ = 53-5 = 48$

So, the correct answer is $(D).$

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