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. \text{AMIT: T T F F T T F T T F}
\text{BENN: T T T F F F T T F T}
\text{CHITRA: T T T F T F F T T T}
If Amit and Benn both score 35 marks each then Chitra’s score will be:

• A. 10
• B. 15
• C. 20
• D. 25
• E. None of the above

Hint:

When multiple candidates have almost identical scores in True/False tests, identify the one differing answer. That gives the correct/wrong distribution, which can then be applied to calculate other students’ marks.

Answer 1

The Correct Option is A

Step 1: Understand the scoring system
- Each correct answer = +4 marks
- Each wrong answer = -1 mark
- Total questions = 10


Step 2: Given condition for Amit and Benn
Amit and Benn both score 35 marks.
Let the total number of correct answers for each = \(C\). Then, the number of wrong answers = \(10 - C\).
So, total marks = \(4C - (10 - C) = 5C - 10\).
\[ 5C - 10 = 35 \quad \Rightarrow \quad 5C = 45 \quad \Rightarrow \quad C = 9 \] Thus, both Amit and Benn have 9 correct and 1 wrong answer.

Step 3: Identify the correct answers
- Since both Amit and Benn got 9 correct, the only question where they differ must be the

wrong answer.
- Looking at their answers:
Amit: T T F F T T F T T F
Benn: T T T F F F T T F T
Clearly, in

Question 3, Amit wrote F, Benn wrote T. One of them is wrong, all others are correct. Hence:
- The correct answer for Q3 is either T or F.
- But since they both scored equally, whichever it is, both end up with exactly 9 correct.

Step 4: Evaluate Chitra’s answers
Chitra: T T T F T F F T T T
Now compare with actual correct answers:
- 9 answers are correct (common with Amit and Benn).
- 1 is wrong (the one they differ on).
So we count Chitra’s score by comparing with that set: She gets only 3 correct (so \(3 \times 4 = 12\)) and 7 wrong (\(7 \times -1 = -7\)).
Total score = \(12 - 7 = 5\). But wait — check alignment carefully: Out of 10, Chitra mismatches 6. So final = 10 marks. \[ \boxed{10} \]