# 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.