In an examination, a student is given 4 marks for every correct answer and 2 marks are deducted for every wrong answer. If a student answered all 75 questions and scored a total of 150 marks, then how many questions did that student answer correctly?

Correct option is C

Given:

- Total questions answered = 75

- Correct answers = x

- Wrong answers = 75 - x

- Marks for a correct answer = +4

- Marks deducted for a wrong answer = -2

- Total marks = 150

Formula Used:

$$\text{Total Marks} = (\text{Correct Answers} \times 4) + (\text{Wrong Answers} \times -2)$$​

Substitute (Wrong Answers) = 75 - x :

Total Marks $$= (x \times 4) + ((75 - x) \times -2)$$​

Solution:

Expand the equation:

150 = 4x - 2(75 - x)

150 = 4x - 150 + 2x

Combine like terms:

150 + 150 = 6x

300 = 6x

Solve for x :

x = $$\frac{300}{6}$$​

x = 50

Answer:

C. 50