In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all…

The correct option is B - 81.

Solution

Let the number of correct answers be x and the number of wrong answers be y. Since the student attempted all questions, the total number of questions is ($x + y$x+y).

Step 1: Formulate equations based on the given conditions.
Case 1: 5 marks for correct, 2 marks deducted for wrong. Score = 69.
$5x - 2y = 69$5x−2y=69 - (Equation 1)

Case 2: 4 marks for correct, 1 mark deducted for wrong. Score = 84.
$4x - 1y = 84$4x−1y=84 - (Equation 2)

Step 2: Solve the system of linear equations.
From Equation 2, we can express y in terms of x:
$y = 4x - 84$y=4x−84

Substitute this value of y into Equation 1:
$5x - 2(4x - 84) = 69$5x−2(4x−84)=69
$5x - 8x + 168 = 69$5x−8x+168=69
$-3x = 69 - 168$−3x=69−168
$-3x = -99$−3x=−99
$x = 33$x=33

Now, find the value of y using $x = 33$x=33:
$y = 4(33) - 84$y=4(33)−84
$y = 132 - 84$y=132−84
$y = 48$y=48

Step 3: Calculate the total number of questions.
Total questions = $x + y$x+y
Total questions = $33 + 48 = 81$33+48=81.

Why the other options are incorrect

• Option (a) - 99: This value does not satisfy the simultaneous equations; if total questions were 99, the scores would not align with the 69/84 results given.
• Option (c) - 84: This is the score mentioned in the second scenario, not the total number of questions.
• Option (d) - 79: This value results from a calculation error or incorrect substitution in the linear equations.

Key Concept

Solving a system of linear equations in two variables to determine unknown quantities based on multiple scoring scenarios.