Question:medium

In an examination,there were 75 questions.3 marks were awarded for each correct answer,1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question.Rayan scored a total of 97 marks in the examination.If the number of unattempted questions was higher than the number of attempted questions,then the maximum number of correct answers that Rayan could have given in the examination is

Updated On: Jan 15, 2026
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Solution and Explanation

Given:
- Total questions: \(75\)
- Marks for a correct answer: +3
- Marks for a wrong answer: -1
- Marks for an unattempted question: +1

Definitions:
\(C\) = Number of correct answers
\(W\) = Number of wrong answers
\(U\) = Number of unattempted questions

Formulated Equations:
\(C + W + U = 75 \quad \text{(Equation 1)}\)
\(3C - W + U = 97 \quad \text{(Equation 2)}\)
Also given: \(U>C + W\)

Step 1: Isolate \(U\) from Equation 1
\(U = 75 - C - W\)

Step 2: Substitute \(U\) into Equation 2
\(3C - W + (75 - C - W) = 97\)
\(2C - 2W + 75 = 97\)
\(2C - 2W = 22\)
\(C - W = 11 \quad \text{(Equation 3)}\)

Step 3: Analyze the inequality
Given: \(U>C + W\)
Substitute \(U\) from Equation 1: \(75 - C - W>C + W\)
Rearrange: \(75>2C + 2W\)
Simplify: \(37.5>C + W\)
Therefore: \(C + W<38 \quad \text{(Equation 4)}\)

Step 4: Solve for \(W\) and \(C\) using Equations 3 and 4
From Equation 3: \(C = W + 11\)
Substitute this into Equation 4: \((W + 11) + W<38\)
\(2W + 11<38\)
\(2W<27\)
\(W<13.5\)
Since \(W\) must be an integer, the maximum value for \(W\) is 13.

Calculate the maximum value for \(C\) using \(C = W + 11\). When \(W = 13\), \(C = 13 + 11 = 24\).

Final Result:
The maximum number of correct answers Rayan could have obtained is 24.
Correct Option: 24

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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