math

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

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  1. 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.

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  2. 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

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