Answer :
[tex]\huge{\bf{{\underline{\colorbox{red} {\color{black} {Answer}}}}}}[/tex]
1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?
To solve this, we need to find the number of questions the student answered correctly.
Given information:
- The student answered 120 questions and got 90 marks.
- One mark is awarded for every correct answer, and $\frac{1}{4}$ mark is deducted for every wrong answer.
Let's assume the student answered $x$ questions correctly.
Total marks obtained = $x - (120 - x) \times \frac{1}{4}$
90 = $x - (120 - x) \times \frac{1}{4}$
90 = $x - 30 + \frac{x}{4}$
90 = $1.25x - 30$
120 = $1.25x$
$x = 96$
Therefore, if the answer to all questions he attempted by guessing were wrong, the student answered $\textbf{96 questions correctly}$.
2. How many questions did he guess?
The total number of questions the student answered is 120, and the number of questions he answered correctly is 96.
Number of questions he guessed = 120 - 96 = 24
Therefore, the student guessed $\textbf{24 questions}$.
3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?
Given information:
- The student answered 80 questions correctly.
- The answer to all questions he attempted by guessing were wrong.
Marks obtained = 80 - (120 - 80) × $\frac{1}{4} $= 80 - 10 = 70 marks
Therefore, the student got $\textbf{70 marks}$.
4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?
Given information:
- The answer to all questions he attempted by guessing were wrong.
- The student scored 95 marks.
Let's assume the student answered $x$ questions correctly.
Total marks obtained = $x - (120 - x) \times \frac{1}{4}$
95 = $x - (120 - x) \times \frac{1}{4}$
95 = $x - 30 + \frac{x}{4}$
95 = $1.25x - 30$
125 = $1.25x$
$x = 100$
Therefore, the student answered $\textbf{100 questions correctly}$ to score 95 marks.