Q. In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect response ?
(a) 9
(b) 13
(c) 27
(d) 43
Correct Answer: (a) 9
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
Correct and Incorrect Answers Calculation
Let’s say the student answered x questions correctly and y questions incorrectly. Since the student attempted all 90 questions, we can write the equation x + y = 90.
For every correct answer, the student gets 5 marks and for every incorrect answer, 2 marks are deducted. So the total marks obtained by the student can be calculated as 5x – 2y. According to the question, this is equal to 387. So we can write another equation: 5x – 2y = 387.
Now we have a system of two equations with two unknowns: x + y = 90 & 5x – 2y = 387
Solving this system of equations gives us x = 81 and y = 9. So the student answered 9 questions incorrectly.