Question:medium

In an examination there are 30 questions. 1 mark is given for each correct answer and 0.25 is deducted for every incorrect answer. Ankur attempted all the questions and scored 13.75. How many incorrect answers did he have?

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Set up c + w = 30 and c - 0.25w = 13.75, then solve the pair of equations for w.
Updated On: Jul 10, 2026
  • 10
  • 11
  • 12
  • None of the above.
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The Correct Option is D

Solution and Explanation

Step 1: Start from a perfect score.
If Ankur had answered all 30 questions correctly, his score would be 30, since each correct answer earns 1 mark and there is no penalty for a right answer.

Step 2: Find how many marks he actually lost.
His real score is 13.75, so compared to a perfect score he lost
$30 - 13.75 = 16.25$ marks.

Step 3: Work out what one wrong answer costs him.
Swapping one correct answer for one wrong answer does two things at once: it removes the 1 mark he would have earned, and it adds a 0.25 mark penalty.
So each wrong answer costs him $1 + 0.25 = 1.25$ marks compared to the perfect score.

Step 4: Divide the total loss by the cost per wrong answer.
Number of wrong answers $= \dfrac{16.25}{1.25} = 13$.

Step 5: Match with the given choices.
13 is not among 10, 11, 12 or 15, so none of the listed numbers work.

Final Answer:
Ankur had 13 incorrect answers, so the correct choice is option E, none of the above. \[ \boxed{13} \]
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