In a test, a correct answer gives 4 marks and a wrong answer gives −1 mark. Out of 20 questions, the total score is 55. How many answers are correct?

15

The governing idea is to model the numbers of correct and wrong answers as two linear equations. Let c be the number of correct answers and w the number of wrong answers. Since all 20 questions are counted, c + w = 20. The marking rule gives 4c − w = 55, because each wrong answer contributes negative one mark. Adding the two equations eliminates w: 5c = 75, so c = 15. Then w = 20 − 15 = 5, and the score check is 15 × 4 − 5 × 1 = 60 − 5 = 55. Thus option C is correct. Options A, B and D would produce scores 47, 52 and 61 respectively when the remaining answers are treated as wrong, so they fail the given total.

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..