Question

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers, what is her score?
(iii) Heena gets two correct answers and five incorrect answers out of seven questions she attempts. What is her score?

Answer 1

Hint: Let us say for any student who gave x right questions and y wrong questions, his total marks is given as 5x + (−2)y i.e. 5x − 2y total marks. Now, for every case, substitute the number of right answers and number of wrong answers in this linear equation and solve to find the final answer.

Complete step by step answer:
In this question, we are given that in a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers.
(ii) Reshma gets five correct answers and five incorrect answers.
(iii) Heena gets two correct answers and five incorrect answers out of seven questions she attempts.
We need to find the scores of these students.
We will just forget unattempted questions as it will give her 0 marks
Let us say for any student who gave x right questions and y wrong questions, his total marks is given as 5x + (−2)y i.e. 5x − 2y total marks.
Mohan gets 4 correct and 6 incorrect answers. So, his total score is $5\times 4-2\times 6=8$ marks
Reshma gets 5 correct answers and 5 incorrect answers. So, her total score is $5\times 5-2\times 5=15$ marks.
Heena gets 2 correct answers and 5 incorrect. She attempts only 7 questions so for the remaining 3 questions she will score zero marks. So, her total score is $5\times 2-2\times 5+0=0$ marks.
Hence, (i) Mohan scores 8 marks
(ii) Reshma scores 15 marks, and
(iii) Heena scores 0 marks.

Note: In this question, it is advisable to form a linear equation in two variables: number of right answers and number of wrong answers. This way, you only have to put the values from the three cases into the linear equation instead of calculating separately for each part. This will save you a lot of time and effort.