Question

In a test, +3 marks are given for every correct answer and \[ - 1\] marks are given for every incorrect answer. Sona attempted all the questions and scored \[ + 20\] marks though she got 10 correct answers.
(i). How many incorrect answers has she attempted?
(ii). How many questions were given in the test?

Answer 1

Hint: To solve this question first we assume a variable as a total number of terms. Then out of the 10 are correct and the remaining are incorrect. Then we make equations according to the obtained marks and the marks of correct answers and marks of incorrect answers. Then solve that equation to get a total number of questions. Then subtract a correct number of answers to get an incorrect number of answers.

Complete step-by-step solution:
Given,
Marks of the correct answer is \[ + 3\]
Marks of the incorrect answer is \[ - 1\]
The total obtained marks are \[ + 20\] and the correct number of answers is 10.
To find,
Find the number of incorrect answers and the total number of questions.
To solve this question first we assume a total number of questions.
Let the total number of questions \[x\]
Total number of correct answers 10
The total number of incorrect answers are \[x - 10\]
So marks obtained by correct answers are \[10 \times 3\] because \[ + 3\] marks for each correct answer
Marks lost by the incorrect answers are \[\left( {x - 10} \right) \times - 1\] because \[ - 1\] for each incorrect answer.
\[\text{Total obtained marks} = \text{Marks obtained by correct answer}{\text{ + }}\text{marks loose by incorrect answer}\]
On putting all the values
\[20 = 30{\text{ + }}\left( {x - 10} \right) \times - 1\]
On further solving
\[x - 10 = 30 - 20\]
\[x = 10 + 10\]
On simplifying
\[x = 20\]
(ii) Total number of questions are
\[ \Rightarrow x = 20\]
(i)\[\text{Total number of incorrect answers} = \text{Total number of questions}-\text{Total number of correct answers}\]
\[\text{Total number of incorrect answers} = 20- 10\]
Total number of incorrect answer are 10.

Note: If in question it is not given that all questions are attempted then we have to assume two variables and make an equation on both the variables and then solve them to get the values of the total number of questions, and more questions that are asked in the question.