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Question:

In a True/False quiz, 4 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer. Amit, Benn and Chitra answered the same 10 questions, and their answers are given below in the same sequential order.

AMIT      T T F F T T F T T F
BENN     T T T F F T F T T F
CHITRA  T T T T F F T F T T

If Amit and Benn both score 35 marks each then Chitra’s score will be:

Explanation:

The correct answer fetches 4 marks whereas the wrong answer fetches -1 marks.

Amit scored 35 marks each in these 10 questions.

Let the number of correct answers be ‘c’ and wrong answers be ‘w’
4c – w = 35
c + w = 10
⇒ c = 9, w = 1, which means 9 correct answers and 1 wrong.

∴ Both Amit and Ben gave 1 wrong answer each.

Amit and Ben marked different answers for 3^rd and 5^th questions.

⇒ Amit and Ben would’ve answered 3^rd or 5^th question wrong in any order.
∴ They marked all other answers correctly.

⇒ Chitra marked correct answers for 3 questions (i.e., 1^st, 2^nd and 9^th)

Out of 3^rd and 5^th questions marked by Chitra one would be correct and the other wrong.

Hence, Chitra marks 4 answers correctly and remaining 6 were wrong.

∴ Chitra’s score = 4 × 4 – 6 × 1 = 10.

Hence, option (a).