Question

. In a competitive examination, one mark is awarded for each correct answer, while ½ mark is deducted for each wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Answer 1

Number of correct answers: 100.

Explanation:

Assume that Jayanti got all 120 questions right. She will score 120 marks if the assumption is true. However, for each answer that she got wrong, this assumption will overestimate her score by (1 - (1/2)) = 3/2 marks.

The real score is 90. That's 30 marks below the expected 120 marks. How many incorrect answers does it take to reduce the expected score by 30 marks? In other words, how many 3/2 are there in 30?

`\displaystyle (120 - 90)/((3)/(2)) = (30)/((3)/(2)) = (30* 2)/(3) = 20`.

It will take 20 wrong answers to cause the score to fall from by 30 marks. In other words, Jayanti got 20 wrong answers out of the 120 questions she answered. The rest of the 120 - 20 = 100 answers are correct.