​In a competitive examination 1 mark is awarded for a correct answer, 0 marks for an unattempt question and $$\frac{1}{2}$$​ mark is deducted for every wrong answer. Ambika answered 120 questions and got 90 marks. How many answers were correct?​

Correct option is C

Given:

Total questions attempted by Ambika = 120

Marks for a correct answer = +1

Marks for an unattempted question = 0

Marks deducted for a wrong answer = $$-\frac{1}{2}$$​​

Total marks obtained = 90

Solution:

Let, x be the number of correct answers.

y be the number of wrong answers.

Since all questions are either correct or wrong (none are unattempted):

x + y = 120

The total marks equation:

​$$x - \frac{1}{2} y = 90$$​​

From the first equation:

y = 120 − x

​$$x - \frac{1}{2} (120 - x) = 90$$​​

​$$x - \frac{120}{2} + \frac{x}{2} = 90$$​​

​$$x - 60 + \frac{x}{2} = 90$$​​

​$$x + \frac{x}{2} = 150$$​​

​$$\frac{2x + x}{2} = 150$$​​

​$$\frac{3x}{2} = 150$$​​

3x = 300

x = 100

Option (C) is right.