In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 120 questions and scored 320 marks. Find the number of questions, he answered incorrectly.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
All 120 questions were attempted, so correct + wrong = 120, and the score is 3 marks for each correct answer minus 1 mark for each wrong one.
The score (3 marks on each of the \(120-w\) correct answers, less 1 mark on each of the \(w\) wrong ones):
Let the wrong answers be \(w\); the correct answers are \(120-w\)
Score: \(3(120-w)-w=320\)
Finding \(w\) (each wrong answer costs 4 marks against the full 360: 3 not earned and 1 taken away):
\(360-4w=320\)
40 marks are lost, so \(4w=40\)
\(w=10\)