Directions : Read the pie chart carefully and answer the following question.…
2023
Directions : Read the pie chart carefully and answer the following question.
Pie chart given below shows the percentage distribution of questions attempted by four different (A, B, C and D) students in an exam. Exam contains three subjects English, History and Mathematics which consist of 120, 60 and 100 questions respectively.
Maximum number of questions attempted by each student is 240 and total number of questions attempted by all the students is 800.
For each incorrect question one mark is deducted and for each right answer two marks is given. If A attempted 30% of the total questions attempted by him in History and gained 66 marks from History, then find the number of incorrect questions attempted by A in History.
- A.
18
- B.
15
- C.
20
- D.
None of these
- E.
42
Show answer & explanation
Correct answer: A
Concept
In a +2 / −1 scoring scheme, if a student attempts n questions of which c are correct and w are wrong, then two independent relations hold: the count relation c + w = n and the score relation 2c − w = marks. Solving these two linear equations gives the number of correct and incorrect attempts. The percentage from the pie chart only fixes how many questions the student attempted in total.
Applying it to A
From the pie chart, A attempted 25% of all the questions attempted by everyone. Total attempted by all = 800, so A attempted 25% of 800 = 200 questions.
A attempted 30% of his own total in History: 30% of 200 = 60 questions (this equals the full 60-question History paper, which is consistent).
Let correct = c and incorrect = w. Count relation: c + w = 60.
Score relation: each correct gives +2 and each wrong takes −1, and the total from History is 66, so 2c − w = 66.
Add the two equations to eliminate w: (2c − w) + (c + w) = 66 + 60, i.e. 3c = 126, so c = 42.
Therefore incorrect = 60 − 42 = 18.
Cross-check
Plug back: 42 correct give 42 × 2 = 84 marks, 18 wrong take 18 × 1 = 18 marks, net = 84 − 18 = 66 marks. This matches the given score, so the number of incorrect questions is 18.