Question

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Answer 1

Total answers = 120
Let the number of correct answers = x
Hence, number of wrong answers = 120-x
Now, marks awarded for x right answer = ​​​​​​​​​​​​​​x $\times$ 1 = x
and marks deducted for (120-x) wrong answers = ​​​​​​​(120-x) $\times$ 0.5 = 60 - 0.5​​​​​​​x
Total marks scored = Marks awarded for right answers - marks deducted for wrong answers
= x - (60 - 0.5 x)

= 1.5x - 60

As per the question, 1.5​​​​​​​x - 60 = 90
⇒ 1.5​​​​​​​x= 150
⇒​​​​​​​ x = 100
So, the number of correct answers is 100.