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 responses?

The correct option is 9 (Option 1).

Step-by-Step Explanation:

Let us define the variables for the given problem:

Let $x$ be the number of correct responses.

Let $y$ be the number of incorrect (wrong) responses.

Step 1: Set up the total questions equation

The student attempted all 90 questions. Therefore, the total number of questions is the sum of correct and incorrect responses:

$x+y=90$

From this equation, we can express $x$ in terms of $y$:

$x=90-y$    --- (Equation 1)

Step 2: Set up the total marks equation

The marking scheme gives 5 marks for every correct answer and deducts 2 marks for every wrong answer. The total marks obtained by the student is 387.

$5x-2y=387$    --- (Equation 2)

Step 3: Solve for the number of incorrect responses ($y$)

Substitute Equation 1 into Equation 2:

$5(90-y)-2y=387$

Expand the terms:

$450-5y-2y=387$

Combine like terms:

$450-7y=387$

Rearrange the terms to solve for $y$:

$7y=450-387$

$7y=63$

$y=\frac{63}{7}$

$y=9$

Therefore, the number of incorrect responses is 9.