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 any question. Rakesh scores 18 marks by attempting16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly? [4 MARKS]

Answer 1

Interpretating the question : 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

(Number of correct answers)(3) + (Number of incorrect answers)(-2) = 18

$\Rightarrow$ (Number of correct answers)(3) + (16 - Number of correct answers)(-2) = 18

$\Rightarrow$ (Number of correct answers)(3) + -32 + 2(Number of correct answers) = 18

$\Rightarrow$ (Number of correct answers)(5) + -32 = 18

$\Rightarrow$ (Number of correct answers)(5) = 18 + 32 =50

$\Rightarrow$ Number of correct answers=10

$\therefore$ Number of incorrect answers=16 - 10=6

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