Question

In a class test (+3) marks are given for every correct answer and (−2) marks are given for every incorrect answer and no marks for not attempting a question. Rakesh scores 18 marks by attempting 16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly? [4 MARKS]

Answer 1

Writing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark

Marks obtained for 1 right answer = +3

Marks obtained for 1 wrong answer = −2

Total marks scored by Rakesh = 18

Number of questions attempted = 16

(No. of correct ans)(3) + (No. of incorrect ans)(-2)
= 18

$\Rightarrow$ (No. of correct ans)(3) + (16 - No. of correct ans)(-2)
= 18

$\Rightarrow$ (No. of correct ans)(3) + -32 + 2(No. of correct ans)
= 18

$\Rightarrow$ (No. of correct ans)(5) + -32 = 18

$\Rightarrow$ (No. of correct ans)(5) = 18 + 32 = 50

$\Rightarrow$ No. of correct ans = 10

$\therefore$ No. of incorrect ans = 16 - 10 = 6

$\therefore$ Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively.