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10. In a test, [tex]$(+3)$[/tex] marks are given for every correct answer and [tex]$(-1)$[/tex] mark is given for every incorrect answer. Sona attempted all the questions and scored [tex]$(+20)$[/tex] marks even though she got 10 correct answers.

(i) How many incorrect answers did she attempt?
(ii) How many questions were given in the test?


Sagot :

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.