There are 100 questions in which each right answer has 1 mark credit. Out of 100 questions 30, 50 and 20 questions are easy, medium and difficult respectively. The question paper covers five abilities with an equal number of questions and similar distribution of difficulty levels for each ability. Sachin has excellent knowledge in three abilities but in the other two abilities he can solve only easy questions. If the evaluator deducts 0.33 marks for each wrong answer and Sachin attempts all questions, which of the following would be his expected score?

LohaHridoy
  1. 62.60
  2. 62.98
  3. 62.76
  4. 62.49

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AhmedNazir

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Option 3 : 62.76

Given

Total number of questions = 100

Marks awarded for right answer = 1

Marks deducted for wrong answer = 0.33

  Ability 1 Ability 2 Ability 3 Ability 4 Ability 5
Easy(30 questions) 6 6 6 6 6
Medium(50 questions) 10 10 10 10 10
Difficult(20 questions) 4 4 4 4 4

 

Calculation

Sachin answered right in First three abilities and all question from easy category. it means his right answered was (6 × 5) + (10 × 3) + (4 × 3)

⇒ 30 + 30 + 12

⇒ 72 

Sachin gave wrong answer to the question of 4 and 5 level from medium and difficult category = (10 × 2) + (4 × 2)

⇒ 20 + 8

⇒ 28

Marks scored by Sachin = 72 × 1 - (28 × 0.33)

⇒ 72 - 9.24

⇒ 62.76

∴ Sachin expected score is 62.76.

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