Question

In an examination, a candidate had to answer $25$ questions each requiring a single answer 'True' or 'False'. It was marked by giving $2$ marks for each correct answer and $-1$ for each incorrect answer.

Use your formula to find out how many of his answer were correct, if he answered all the questions and scored a total of $2$ marks.

Answer 1

There are total of $25$ questions to be answered.

Lets true answers be $x$, then false answers are $(25-x)$.
As per the question, number are $2x$ or $-1(25-x)$
So, $2x-(25-x)=2$
$\therefore 2x+x=2+25$
$\therefore 3x=27$
$\therefore x=9$