Question

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​

Answer 1

Answer :-

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