The correct option is B - 81.
[as per provisional answerkey]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).
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 - (Equation 1)
Case 2: 4 marks for correct, 1 mark deducted for wrong. Score = 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
Substitute this value of y into Equation 1:
5x−2(4x−84)=69
5x−8x+168=69
−3x=69−168
−3x=−99
x=33
Now, find the value of y using x=33:
y=4(33)−84
y=132−84
y=48
Step 3: Calculate the total number of questions.
Total questions = x+y
Total questions = 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.