Question

Deepthi scored 80 marks in a test, getting 5 marks for each right answer and losing 2 marks for each wrong answer. If the number of wrong answers is 5 more than her number of correct answers, then how many questions did she answer correctly and wronlgy?
(3 marks)

Answer 1

Let number of questions answered correctly be $x$.
Number of questions answered wrong $=x+5$
(0.5 marks)

⇒ Marks obtained for the correct answers $=5x$
⇒ Marks deducted for the wrong answers $=2\times (x+5)$
(0.5 marks)

⇒ Marks scored = (marks for correct answers - marks for wrong answers)
(0.5 marks)

$\Rightarrow 80=5x-2(x+5)$
$\Rightarrow 80=5x-2x-10$
$\Rightarrow 90=3x$
$\Rightarrow x=30$
(1 mark)

$\therefore$ the number of questions that she answered correctly is, $x=30$
the number of questions that she answered wrongly is, $x+5=35$
(0.5 marks)