A test comprises of 200 questions. Each correct answer carried 2 marks. Each wrong answer carried -1/2 mark and unanswered questions carried no marks. Ajay attempted all the questions in the test and scored 360 marks. What would be his marks, if each answer carried only 1/2 mark and each wrong answer carried -2 marks ? explain correctly step by step pls the correct answer is 60
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Let the number of question he answered correctly be x and number of question he answered wrong be y.
Total questions = 200
→ x + y = 200
Now, marks for correct answer is +2 and for incorrect is - ½.
Marks scored by him = 360
→ 2x + ( - ½ y ) = 360
Now we have two equations :-
→ x + y = 200 -i
→ 2x - ½ y = 360 -ii
Mutiplying equation i by 2 :-
→ 2x + 2y = 400 -iii
Subtracting equation ii from iii :-
→ 2x + 2y - ( 2x - ½ y ) = 400 - 360
→ 2x + 2y - 2x + ½ y = 40
→ 2y + ½ y = 40
→ 5/2 y = 40
→ 5y = 80
→ y = 80 / 5
→ y = 16
Substituting the value in equation i
→ x + y = 200
→ x + 16 = 200
→ x = 184
Number of questions he answered correctly = 184
Number of questions he answered incorrectly = 16
According to the question -
- Right answer carry ½ marks
- Wrong answer carry - 2 marks
So, total marks = 184 × ½ - 2 × 16
= 92 - 32
= 60
Total marks scored by him = 60 mark
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