Question

There are 40 questions in the test booklet of mathematics olympiad if stephen attempts all the questions and scores 80 marks when 5 marks are awarded for each correct answer and 3 marks is deducted for each incorrect answer then find the number of correct answers

Answer 1

Let us assume the correct answers as "x" and wrong answers as "y".

According to question,

(i) Total number of questions in the test:

⇒ x + y = 40 .

(ii) 5 marks are awarded for correct answer and 3 marks for wrong answer. He scores 80 marks.

⇒ 5x - 3y = 80  

On solving (i) * 5 & (ii), we get

⇒ 5x + 5y = 200

⇒ 5x - 3y = 80

   -------------------

            8y = 120

             y = 15.

Substitute y = 15 in (ii), we get

⇒ 5x - 3y = 80

⇒ 5x - 45 = 80

⇒ 5x = 125

⇒ x = 25.

Therefore:

⇒ Number of correct answers = 25

⇒ Number of incorrect answers = 15.

The answer is Option(D) - 25.

Hope it helps!

Answer 2

heya...

here is your answer..

If Stephen attempted all questions...  

Let no. of correct answers be a and no. of incorrect answer be b.  

So, a + b = 40.  

5a - 3b = 80.  

=>a= 25 and b= 15.

it may help you..