Question

In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer.
i. Radhika answered all the questions, scored 30 marks and got 10 correct answers
ii. Jay also answered all the questions, scored (-12) marks though he got 4 correct answers.
How many incorrect answers had they attempted?

• A. 22
• B. 24
• C. 26
• D. 28

Answer 1

The correct option is C 26

Marks awarded for one correct answer = +5
Marks awarded for one incorrect answer = -2
Total score = Marks obtained for correct answers - Marks obtained for incorrect answers
Its given that both Radhika and Jay have answered all the questions.

Radhika scored 30 marks and got 10 correct answers.
Let x be the number of questions answered incorrectly by Radhika.
$\Rightarrow$ 30 = (+5) $\times$ (10) - 2 $\times$ x
$\Rightarrow$ 30 = 50 -2x
$\Rightarrow$ 2x = 50 -30
$\Rightarrow$ 2x = 20
$\Rightarrow$ x =10

Jay scored -12 marks and got 4 correct answers.
Let y be the number of questions answered incorrectly by Radhika.
$\Rightarrow$ -12 = (+5) $\times$ (4) - 2 $\times$ y
$\Rightarrow$ -12 = 20 -2y
$\Rightarrow$ 2y = 20 + 12
$\Rightarrow$ 2y = 32
$\Rightarrow$ y = 16
Now, total number of incorrect answers = 10 + 16 = 26