In an exam, the objective type test contains a total of 80 questions. Every correct answer award 2.5 marks and 1/3rd of the marks of question are deducted for every wrong answer. After attempting 40 questions, a student secured total of 66.67 marks. How many of incorrect answers are attempted by the student?

(a) 12

(b) 13

(c) 10

(d) 09

Question

In an exam, the objective type test contains a total of 80 questions. Every correct answer award 2.5 marks and 1/3rd of the marks of question are deducted for every wrong answer. After attempting 40 questions, a student secured total of 66.67 marks. How many of incorrect answers are attempted by the student?

(a) 12

(b) 13 

(c) 10 

(d) 09

ONLiNE UPSC · Accepted Answer

Let the number of correct answers be x. 

Then the number of incorrect answers is 40 &minus; x, since the student attempted 40 questions in total. 

Each correct answer gives 2.5 marks, so total marks from correct answers = 2.5x 

For every wrong answer, 

1/3 of 2.5 marks is deducted, which is 5/6. 

So, total penalty for incorrect answers = 5/6 &times; (40 &minus; x). 

The student&rsquo;s final score is 66.67 marks. 

Therefore, the equation becomes:

2.5x &ndash; 5/6 &times; (40&minus;x) = 66.67 

On solving,

x = 30.001

Since the result is approximately 30, the student answered 30 questions correctly, and hence:

40 &ndash; 30 = 10 incorrect answers.

 

Hence option c is correct.

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