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A unit test paper contains 20 questions. Students are awarded 3 marks for each correct answer, -1 mark for each incorrect answer, and 0 marks for not attempting the question.

i) Anushka gets eight correct and twelve incorrect answers. What is her score?

ii) Twisha gets ten correct answers and ten incorrect answers. What is her score?

iii) Natasha gets four correct answers and her score is 5. How many questions did she answer incorrectly?



Answer :

GinnyAnswer
Let's break down each part of the question step-by-step:

### i) Anushka's Score Calculation

Anushka answered 8 questions correctly and 12 questions incorrectly.
- For each correct answer, she gets 3 marks.
- For each incorrect answer, she loses 1 mark.

Her total score can be calculated as follows:
[tex]\[ \text{Anushka's Score} = ( \text{Number of Correct Answers} \times 3 ) + ( \text{Number of Incorrect Answers} \times (-1) ) \][/tex]
[tex]\[ \text{Anushka's Score} = ( 8 \times 3 ) + ( 12 \times (-1) ) \][/tex]
[tex]\[ \text{Anushka's Score} = 24 - 12 \][/tex]
[tex]\[ \text{Anushka's Score} = 12 \][/tex]

So, Anushka's score is 12.

### ii) Twisha's Score Calculation

Twisha answered 10 questions correctly and 10 questions incorrectly.
- For each correct answer, she gets 3 marks.
- For each incorrect answer, she loses 1 mark.

Her total score can be calculated as follows:
[tex]\[ \text{Twisha's Score} = ( \text{Number of Correct Answers} \times 3 ) + ( \text{Number of Incorrect Answers} \times (-1) ) \][/tex]
[tex]\[ \text{Twisha's Score} = ( 10 \times 3 ) + ( 10 \times (-1) ) \][/tex]
[tex]\[ \text{Twisha's Score} = 30 - 10 \][/tex]
[tex]\[ \text{Twisha's Score} = 20 \][/tex]

So, Twisha's score is 20.

### iii) Natasha's Incorrect Answers Calculation

Natasha got 4 questions correct and her total score is 5.
- For each correct answer, she gets 3 marks.
- For each incorrect answer, she loses 1 mark.

We need to find how many questions she answered incorrectly. Let [tex]\( x \)[/tex] be the number of incorrect answers.

We can use the given information to set up the equation:
[tex]\[ \text{Natasha's Score} = ( \text{Number of Correct Answers} \times 3 ) + ( \text{Number of Incorrect Answers} \times (-1) ) \][/tex]
[tex]\[ 5 = ( 4 \times 3 ) + ( x \times (-1) ) \][/tex]
[tex]\[ 5 = 12 - x \][/tex]

Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 12 - 5 \][/tex]
[tex]\[ x = 7 \][/tex]

So, Natasha answered 7 questions incorrectly.

In summary:
- Anushka's score is 12.
- Twisha's score is 20.
- Natasha answered 7 questions incorrectly.

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