Answer :
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.
### 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.
