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.
A) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?
B) Mohini scores – 5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

Answer 1

Hint: First, we have to find the total correct marks they got by using the formula i.e. total marks for correct answer = marks for correct answer $ \times $ number of correct answers. Then subtracting those marks from the total mark, they will be marks of incorrect answers. After that, on dividing it with marks given for every negative answer, we get the total number of incorrect answers they have attempted i.e. total marks for incorrect answer = marks for incorrect answer $ \times $ number of incorrect answers.

Complete step by step answer:
Here, we are given positive marks for every correct answer and negative marks for every incorrect answer i.e. for the correct answer $ = + 3$ and for every incorrect answer $ = - 2$ mark.
(i)
Radhika got total marks $ = 20$, the correct answer $ = 12$
So, the total marks for correct answer = marks for correct answer $ \times $ number of correct answers.
$ \Rightarrow $ Total marks for correct answer $ = 3 \times 12$ marks
Multiply the terms,
$ \Rightarrow $ Total marks for correct answer $ = 36$ marks
Thus, Radhika got a total of 36 marks for 12 correct answers.
Now, subtracting the total marks of the correct answer from the total marks we will get marks for incorrect answers. So, writing as
$ \Rightarrow $ Total marks for incorrect answer $ = 20 - 36$ marks
Subtract the values,
$ \Rightarrow $ Total marks for incorrect answer $ = - 16$ marks
So, she got 16 marks for the incorrect answer. Now, we know that for every incorrect answer $ = - 2$ marks.
So, the total marks for incorrect answers = marks for incorrect answer $ \times $ number of incorrect answers.
Substituting values, we get
$ \Rightarrow - 16 = - 2 \times $ number of incorrect answers
So, dividing by $ - 2$ on both sides, we get
$ \Rightarrow $ Number of incorrect answers $ = 8$
Hence, the number of incorrect answers is 8.
(ii)
Mohini got total marks $ = - 5$, the correct answer $ = 7$
So, the total marks for correct answer = marks for correct answer $ \times $ number of correct answers.
$ \Rightarrow $ Total marks for correct answer $ = 3 \times 7$ marks
Multiply the terms,
$ \Rightarrow $ Total marks for correct answer $ = 21$ marks
Thus, Radhika got a total of 21 marks for 7 correct answers.
Now, subtracting the total marks of the correct answer from the total marks we will get marks for incorrect answer. So, writing as
$ \Rightarrow $ Total marks for incorrect answer $ = - 5 - 21$ marks
Subtract the values,
$ \Rightarrow $ Total marks for incorrect answer $ = - 26$ marks
So, she got 26 marks for the incorrect answer. Now, we know that for every incorrect answer $ = - 2$ marks.
So, the total marks for incorrect answers = marks for incorrect answer $ \times $ number of incorrect answers.
Substituting values, we get
$ \Rightarrow - 26 = - 2 \times $ number of incorrect answers
So, dividing by $ - 2$ on both sides, we get
$ \Rightarrow $ Number of incorrect answers $ = 13$

Hence, the number of incorrect answers is 13.

Note: Linear equations are the equations in which the variables are raised to the power equal to one. The linear equations are classified into different types based on the number of variables in the equation. The different types of linear equations are:
Linear equations in one variable are linear equations that consist of only one variable.
Linear equations in two variables are linear equations which consist of two variables.
Linear equations in three variables are linear equations which consist of three variables.