Question

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she attempts in all 50 questions and scores 120 marks, the number of questions she attempts correctly is:
A. 62
B. 44
C. 42
D. 34

Answer 1

Hint: Take ‘x’ as the number of correct answers. Thus find the number of incorrect answers. Formulate an equation based on this and equate it to 120. Thus get the value of x, which is the number of correct answers.

Complete step-by-step answer:
The mark that the student scores for every correct answer = 4 marks.
Similarly, the mark that the student scores for every incorrect answer = 1 mark.
The number of questions she attempted = 50.
The mark scored by the student by attempting 50 questions = 120 marks.
What we need to find is the number of questions that the student attempted correctly.
Let us consider the number of correct answers as x.
As the student attempted 50 questions in all, the number of incorrect answers can be given as \[\left( 50-x \right).\]
\[\therefore \]Number of correct answers = x
\[\therefore \]Number of incorrect answers = \[50-x\]
Thus we can formulate the expression that \[(4\times \]number of correct answers) minus \[(1\times \]number of incorrect answer) will give 120 marks.
\[\begin{align}
  \Rightarrow & \therefore 4x-1\left( 50-x \right)=120 \\
  \Rightarrow & 4x-\left( 50-x \right)=120. \\
\end{align}\]
Now let us solve the above expression and find the value of x.
\[\begin{align}
\Rightarrow & 4x-50+x=120 \\
 \Rightarrow & 4x+x=120+50 \\
\Rightarrow & 5x=170 \\
\Rightarrow & x=\dfrac{170}{5}=34. \\
\end{align}\]
Thus we got the number of correct answers as = x = 34.
\[\therefore \]The number of incorrect answers = 50 – x = 50 – 34 = 16.
Thus the number of incorrect answers is 34.
\[\therefore \]Option D is the correct answer.

Note: Here we have taken \[4x-\left( 50-x \right)=120.\] We should subtract the number of correct answers from the number of wrong answers to get the number of questions attempted correctly. If you are adding the expression, you may get the wrong answer.