Question

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?

• A. 10
• B. 11
• C. 12
• D. None of the above.

Hint:

Set up c + w = 30 and c - 0.25w = 13.75, then solve the pair of equations for w.

Answer 1

The Correct Option is D

Step 1: Set up the two equations.
Let \(c\) be the number of questions Ankur got correct and \(w\) be the number he got wrong. He attempted all 30 questions, so \(c + w = 30\).
Each correct answer adds 1 mark and each wrong answer takes away 0.25 marks, so his score gives \(c - 0.25w = 13.75\).

Step 2: Remove \(c\) from the equations.
From the first equation, \(c = 30 - w\). Put this into the score equation.
\[ (30 - w) - 0.25w = 13.75 \]

Step 3: Solve for \(w\).
\[ 30 - 1.25w = 13.75 \]
\[ 1.25w = 30 - 13.75 = 16.25 \]
\[ w = \frac{16.25}{1.25} = 13 \]

Step 4: Check against the answer choices.
Ankur had \(w = 13\) wrong answers, so he got \(c = 30 - 13 = 17\) right. Check: \(17 - 0.25 \times 13 = 17 - 3.25 = 13.75\), which matches the given score.
The value 13 is not equal to 10, 11 or 12, so those three options fail.

Final Answer:
Since 13 does not appear among the first three choices, the correct choice is option E, none of the above. \[ \boxed{w = 13} \]