Let's solve this problem step-by-step.
Part (a): Calculating Diya's score.
First, we need to determine the number of questions Diya attempted:
- Total questions: 100
- Unattempted questions: 16
So, the number of questions she attempted is:
[tex]\[ \text{Attempted questions} = 100 - 16 = 84 \][/tex]
Out of these 84 questions:
- Correct answers: 70
- Incorrect answers: 14
Each correct answer earns her 3 marks, while each incorrect answer deducts 1 mark. Therefore, the total score can be calculated as follows:
[tex]\[ \text{Score} = (\text{Correct answers} \times 3) - (\text{Incorrect answers} \times 1) \][/tex]
[tex]\[ \text{Score} = (70 \times 3) - (14 \times 1) \][/tex]
[tex]\[ \text{Score} = 210 - 14 \][/tex]
[tex]\[ \text{Score} = 196 \][/tex]
So, Diya's score is 196.
Part (b): Determining Diya's rank status relative to a score of 200.
We are given that securing a score of 200 marks results in the 500th rank. To find out whether Diya is ranked above or below the 500th rank, we need to compare her score with 200:
- If her score is greater than 200, her rank would be above 500 (a better rank).
- If her score is less than or equal to 200, her rank would be below 500 (a worse rank).
Diya's score is 196, which is less than 200. Therefore, Diya will be ranked below 500.
Summary of the answer:
- (a) Diya's score is 196.
- (b) Diya will be ranked below 500.
