In a question paper, there are 150 questions, each question carrying 2 marks. The total marks are 300. For every wrong answer 0.50 marks will be deducted from the scored marks. If a person has to score 270 marks in a paper, how many questions should be answered correctly?
number of correct answers --- x
number of incorrect answers --- 150-x
2x - .5(150-x) = 270
2x - 75 + .5x = 270
2.5x = 345
x = 138
He/she should answer at least 138 questions correctly to have score of at least 270
check:
138(2) - 12(.5) = 270
To find out how many questions should be answered correctly to score 270 marks, we need to consider the scoring system.
Each correct answer scores 2 marks, and for each wrong answer, 0.50 marks are deducted. So, effectively, each wrong answer reduces the score by 2.50 marks (2 marks for the wrong answer and a deduction of 0.50 marks).
To calculate the number of questions that need to be answered correctly, we need to find the difference between the desired score (270 marks) and the potential loss due to wrong answers.
Let's start by calculating the potential loss due to wrong answers. Since each wrong answer deducts 2.50 marks, the total loss can be calculated as follows:
Total Loss = Number of Wrong Answers × Loss per Wrong Answer
To score 300 marks, there are 150 questions in total. Let's assume x represents the number of wrong answers.
So, the number of correct answers would be 150 - x.
Now, let's calculate the potential loss:
Potential Loss = x × 2.50
The final score after deducting the potential loss will be:
Final Score = Total Marks - Potential Loss
Now, equating the final score to the desired score, we have:
270 = 300 - x × 2.50
Simplifying the equation:
270 = 300 - 2.50x
Rearranging the equation by moving the terms involving x to one side:
2.50x = 300 - 270
2.50x = 30
Dividing both sides by 2.50:
x = 30 / 2.50
x = 12
So, to score 270 marks, the person should answer 150 - 12 = 138 questions correctly.