# 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,

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

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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