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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?

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 Answer 100

Given:

Number of question attempted = 120 

Marks received by Ambika = 90 

Marks awarded for correct answer = 1

Marks deducted for wrong answer = 0.5 

Calculation:

Let the number of correct answer be = a 

⇒ Number of wrong answers = 120 - a

Marks for 'a' right answers = a × 1 = a 

Marks deducted for (120 - a) wrong answers = (120 - a) × 0.5 = 60 - 0.5a 

As per the question;

Total marks scored = Marks received for right answers - Marks deducted for wrong answers 

⇒ 90 = a - (60 - 0.5a)

⇒ 1.5a = 150 

⇒ a = 100 

∴ The number of correct answers is 100.

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