A test had 200 questions .Each correct answer carried 2 marks.Each wrong answer carried -1/2 marks and unanswered question fetched no marks .Ajay attempted all the question in the test and he scored 360 marks.What would his marks be, if for each correct answer he got 1/2 marks and for each wrong answer he lost 2 marks?
Explain How the solution can be formed
number correct ---- x
number incorrect ---- 200 - x
number left unanswered--- 0
2x - (1/2)(200 - x) = 360
4x - 200 + x = 720
5x = 920
x = 184
so on his test he got 184 correct and 16 wrong.
check:
184(2) - 16(1/2) = 368 - 8 = 360
with the new scoring system:
score = 184/2 - 2(16) = 92 - 32 = 60
To find out what Ajay's marks would be if he got 1/2 marks for each correct answer and lost 2 marks for each wrong answer, we need to compare the scoring system to the original scoring system and make the necessary adjustments.
Original Scoring System:
- Correct answer: 2 marks
- Wrong answer: -1/2 marks
- Unanswered question: 0 marks
Adjusted Scoring System:
- Correct answer: 1/2 marks
- Wrong answer: -2 marks
- Unanswered question: 0 marks
To calculate Ajay's marks using the adjusted scoring system, we can follow these steps:
1. Calculate the number of correct answers in the original test:
- Total marks = 360
- Mark per correct answer = 2
- Number of correct answers = Total marks / Mark per correct answer = 360 / 2 = 180
2. Calculate the number of wrong answers in the original test:
- Number of wrong answers = Total questions - Number of correct answers = 200 - 180 = 20
3. Calculate the number of marks Ajay would get for correct answers in the adjusted scoring system:
- Mark per correct answer = 1/2
- Number of correct answers for adjusted scoring system = Number of correct answers = 180
- Marks for correct answers = Number of correct answers for adjusted scoring system * Mark per correct answer = 180 * 1/2 = 90
4. Calculate the number of marks Ajay would lose for wrong answers in the adjusted scoring system:
- Mark per wrong answer = -2
- Number of wrong answers for adjusted scoring system = Number of wrong answers = 20
- Marks lost for wrong answers = Number of wrong answers for adjusted scoring system * Mark per wrong answer = 20 * -2 = -40
5. Calculate Ajay's total marks in the adjusted scoring system:
- Total marks in the adjusted scoring system = Marks for correct answers + Marks lost for wrong answers = 90 + (-40) = 50 marks
Therefore, Ajay's marks would be 50 marks if he got 1/2 marks for each correct answer and lost 2 marks for each wrong answer.
To calculate the marks for each scenario, we first need to determine the number of correct answers, the number of wrong answers, and the number of unanswered questions in the test.
Scenario 1: Each correct answer carries 2 marks
Let's assume x represents the number of correct answers.
The total number of questions = 200
So, the number of wrong answers and unanswered questions = 200 - x
Total marks obtained = (2 * x) + (-(1/2) * (200 - x))
Now, we know that Ajay obtained a total of 360 marks.
So, the equation becomes:
360 = (2 * x) + (-(1/2) * (200 - x))
To solve this equation, we can start by simplifying it:
360 = 2x - (1/2) * (200 - x)
Then, we can distribute the factor (-1/2) to the terms inside the parentheses:
360 = 2x - (1/2) * 200 + (1/2) * x
Simplifying further:
360 = 2x - (1/2) * 200 + (1/2) * x
360 = 2x - 100 + (1/2) * x
Now, let's combine like terms:
360 = 2.5x - 100
Move the constant term to the right-hand side:
360 + 100 = 2.5x
Simplify:
460 = 2.5x
Divide both sides by 2.5 to solve for x:
x = 184
So, Ajay answered 184 questions correctly in Scenario 1.
To find Ajay's marks in Scenario 2, where each correct answer carries 1/2 mark:
Marks in Scenario 2 = (1/2) * (Number of correct answers)
Substituting the value we found for x:
Marks in Scenario 2 = (1/2) * 184
Marks in Scenario 2 = 92
Therefore, Ajay's marks in Scenario 2, where each correct answer carries 1/2 mark, would be 92.
200 questions,
2 marks for good answer,
-1/2 marks for wrong answer.
Ajay answered all questions.
If he didn't give any wrong answer, he would have got 400 marks.
Each wrong answer will set him off 2.5 marks.
If he got 360, he got (400-360)/2.5=16 wrong, therefore 184 right.
Now if the rules changed, then 184 correct and 16 incorrect answers would give him
184*0.5-16*2=60 marks.