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Question
In a competitive examination, one mark is awarded for every correct answer while `1/4` mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly? (Use Cramer’s rule to solve the problem).
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Solution
No. of Questions answered = 100
Let the No. of questions answered correctly be x
and the No. of questions answered wrongly be y
Here, x + y = 100 and `x - 1/4 y` = 80
(i.e) x + y = 100 and 4x – y = 320
Δ = `|(1, 1),(1, -1/4)| = - 1/4 - 1 = (-5)/4 ≠ 0`
Δx = `|(100, 1),(80, -1/4)|` = – 25 – 80 = – 105
Δy = `|(1, 100),(1, 80)|` = 80 – 100 = – 20
x = `Delta_x/Delta = (- 105)/((- 5)/4)` = 21 × 4 = 84
y = `Delta_y/Delta = (- 20)/((- 5)/4)` = 4 × 4 = 16
Correct questions = 84
Wrong questions = 16.
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