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 ?

Explanation : 

Objective type test of 90 questions

Given Information:
Total questions = 90
Marks for correct answer = +5
Marks for incorrect answer = -2
Total marks obtained = 387

Let’s solve:
x = number of correct answers
y = number of incorrect answers

Equation 1 (Total Questions):
x + y = 90

Equation 2 (Total Marks):
5x – 2y = 387

Solving the System of Equations:
From Equation 1: x + y = 90
x = 90 – y
Substitute in Equation 2:
5(90 – y) – 2y = 387
450 – 5y – 2y = 387
450 – 7y = 387
-7y = -63
y = 9

Therefore: Incorrect answers = 9
Correct answers = 81 (90 – 9)