In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every wrong answer. Further, 1 mark is to be deducted for every unattempted question. One student receives a total of 46 marks in the examination. However, before releasing the marks, the professor realizes that she has, by mistake, deducted 2 marks for every unattempted question and 1 mark for every wrong answer.
After correction, how many marks will the student get?

Let the number of correct and wrong questions be x and y respectively. 

Number of unattempted questions = 20 - (x+y) $$\longrightarrow\ i$$

4 marks are awarded for every correct questions and 2 and 1 marks are deducted for every wrong and unattempted questions respectively. 

Total original marks scored = 4x-2y-((20-(x+y)) = 5x-y-20 $$\longrightarrow\ ii$$

But the teacher deducted 1 and 2 marks for every wrong and unattempted questions respectively by mistake. 

Total marks = 4x-y-2(20-x-y) = 6x+y-40

Total marks = 46 (given)

6x+y-40 = 46

6x+y = 86 

The possible pairs of (x,y) are (14,2), (13,8), (12,14), ........ , (1,80), (0,86). 

x+y = 16, 21, 26, ........ , 81,86

Only one case will be possible as (x+y) $$\le\ $$ 20 (as equation i $$\ge\ 0$$)

Hence, Number of correct questions = x = 14

Number of wrong questions = y = 2 

Number of unattempted questions = 20 - (14+2) = 4

Hence, final marks = $$\left(5\times\ 14\right)-2-20$$ = 48 (from equation ii) 

$$\therefore\ $$ The required answer is C.