Question

in a competitive examination one mark is awarded for each correct answer why 1/2 mark is deducted for every wrong answer Jayanti answered 120 questions and got 90 marks how many question did she answer correctly

Answer 1

Total answers = 120
Let the number of correct answers = x
number of wrong answers = (120-x)
Marks awarded for each right answer = 1
then Marks awarded for x right answer = x × 1 = x marks
Marks deducted for each wrong answer = 0.5
then marks deducted for (120-x) right answers = (120-x) × 0.5 = 60 - 0.5x
So she will get= marks awarded for right answer - marks deducted for wrong answer
= x - (60-0.5x)
= x - 60 + 0.5x
= 1.5x - 60
And she has got = 90 marks
So
1.5x - 60 = 90
⇒ 1.5x = 90 + 60
⇒ 1.5x = 150
⇒ x = 150/1.5
⇒ x = 100
So she did 100 questions correctly.