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)15
(e)None of these
Answer
Answer (as printed): E
Explanation
Let the number of correct answers be $x$. Then, number of incorrect answers $=(30-x)$. $$\begin{aligned} \therefore \quad x-0.25(30-x) & =13.75 \\ & \Leftrightarrow x-7.5+0.25 x=13.75 \\ & \Leftrightarrow 1.25 x=21.25 \Leftrightarrow x=\frac{2125}{125}=17 . \end{aligned}$$ So, number of incorrect answers $=30-17=13$.
Explanation as extracted from the printed page; notation may be imperfect.