Question

Herman scored 40 marks in a test, getting 4 marks for each right answer and losing 1 mark for each wrong answer. If the number of wrong answers is 1 less than his number of correct answers, then how many questions did he answer correctly?

Answer 1

Let number of questions answered correctly be $x$.

Number of questions answered wrong $=x-1$
Marks obtained for the correct answers $=4x$
Marks deducted for the wrong answers $=1\times (x-1)$
Marks scored = (marks for correct answers - marks for wrong answers)
$\Rightarrow 40=4x-(x-1)$
$\Rightarrow 40=4x-x+1$
$\Rightarrow 39=3x$
$\Rightarrow x=13$

Therefore, the number of questions he has answered correctly is 13.

Verification:
Number of correct answers = 13
Marks obtained for correct answers = 13 x 4 = 52
Number of wrong answers = 13 - 1 = 12
Marks to be deducted for wrong answers = 12 x 1 = 12
Marks scored = (marks for correct answers - marks for wrong answers)
= 52 - 12 = 40.