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In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?​
  • a)
    x + y = 120; 3x + 4y = 80
  • b)
    x + y = 120; 4x + 3y = 80
  • c)
    x + y = 120; – x + 4y = 80
  • d)
    x + y = 60; x + 4y = 80
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In an examination, one mark is awarded for every correct answer, while...
Let the student attempted "y" questions correctly and "x" questions are incorrectly. Assuming he has attempted all questions then,
x + y = 120
For each correct answer he will be awarded 1 mark so the total marks he gets for correct answers is "y". For each wrong answer he will be awarded -1/4 so for total incorrect answers he will be awarded -x/4. He gets 20 marks in total so,
y - x/4 = 20
-x + 4y = 80
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Community Answer
In an examination, one mark is awarded for every correct answer, while...
Let's assume that y questions were answered correctly and x questions were answered incorrectly.
Total no of questions answered =120
Therefore , x+y=120 i.e. equation (1)
Marks awarded for each correct answer =1
=> marks awarded for y correct answers =y
Also , 1/4 marks are deducted for each wrong answer thus , we an say that -1/4 marks are awarded for each incorrect answer.
Thus , marks awarded for x incorrect answers = -x/4
Hence , Total marks obtained = y+(-x/4)= y-x/4
Also , y-x/4= 20 (given)
=> 4y -x =80 (on taking LCM both sides)
i.e. equation (2)
Hence , equation (1) and (2) are the required equations and on solving them ,the values of x and y obtained are 80 and 40 respectively.
Hope it helps !
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In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?a)x + y = 120; 3x + 4y = 80b)x + y = 120; 4x + 3y = 80c)x + y = 120; – x + 4y = 80d)x + y = 60; x + 4y = 80Correct answer is option 'C'. Can you explain this answer?
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