Question

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, what is the number of questions he attempted correctly?
(a). 35
(b). 40
(c). 42
(d). 46

Answer 1

Hint: Assign a variable for correct answers and another variable for wrong answers. Now write down the two equations involving these two variables from the given information and solve them by substitution to get the final answer.

Complete step-by-step answer:
Let the number of questions he answered correctly be x and the number of questions he answered wrongly be y. The total number of questions he attempted is given as 75, then, we have:
\[x + y = 75\]
\[y = 75 - x............(1)\]
The student gains 4 marks for every correct answer and loses one mark for every wrong answer. The total marks he got is 125, then, we have:
\[4x - y = 125\]
Substituting equation (1) into equation (2), we have:
\[4x - (75 - x) = 125\]
Taking the negative sign inside the bracket, we get:
\[4x - 75 + x = 125\]
Adding the x terms and taking – 75 to the right-hand side of the equation, we obtain:
\[5x = 125 + 75\]
We know that 125 added to 75 gives 200. Hence, we have:
\[5x = 200\]
Solving for x by dividing both sides by 5, we have:
\[x = \dfrac{{200}}{5}\]
\[x = 40\]
Therefore, the value of x is 40.
Hence, the number of questions he attempted correctly is 40.
Hence, the correct answer is the option (b).

Note: You can also find the value of the number of questions he attempted wrongly and then substitute to find the number of questions he attempted correctly. The answer is invariant of the order in which we find the variables.