To solve this problem, let's break it down into two parts: finding the number of incorrect answers and the total number of questions.
### Part (i): Finding the number of incorrect answers
We know the following:
- Sona scores [tex]\(+3\)[/tex] marks for each correct answer.
- Sona scores [tex]\(-1\)[/tex] mark for each incorrect answer.
- Sona's total score is [tex]\(+20\)[/tex] marks.
- Sona got 10 correct answers.
First, let's calculate the total marks from the correct answers:
[tex]\[
\text{Marks from correct answers} = 10 \times 3 = 30 \text{ marks}
\][/tex]
Next, let's use the total score to find the marks resulting from incorrect answers. Sona's total score is 20 marks:
[tex]\[
\text{Marks from incorrect answers} = \text{Total score} - \text{Marks from correct answers}
\][/tex]
Substitute the known values:
[tex]\[
\text{Marks from incorrect answers} = 20 - 30 = -10 \text{ marks}
\][/tex]
Since each incorrect answer gives [tex]\(-1\)[/tex] mark, we can find the number of incorrect answers by dividing the marks from incorrect answers by the marks per incorrect answer:
[tex]\[
\text{Number of incorrect answers} = \frac{-10}{-1} = 10
\][/tex]
So, she attempted 10 incorrect answers.
### Part (ii): Finding the total number of questions
The total number of questions Sona attempted is the sum of the correct answers and the incorrect answers:
[tex]\[
\text{Total number of questions} = \text{Correct answers} + \text{Incorrect answers}
\][/tex]
Substitute the known values:
[tex]\[
\text{Total number of questions} = 10 + 10 = 20
\][/tex]
Thus, the total number of questions in the test is 20.
### Summary
(i) Sona attempted 10 incorrect answers.
(ii) The total number of questions in the test was 20.
