Sunita made 4 mistakes in an exam and obtained 75% marks. If she had attempted 6 more questions and made 2 mistakes from these 6 questions, then she would have obtained 85% marks. If all the questions carried equal marks and there was no negative marking for wrong answers, then how many questions were there in the exam?
Explanation:
Let the total number of questions be x.
Let Sunita attempt ‘a’ number of questions correct.
Then, ax = 75100 = 34
⇒ 4a = 3x ...(1)
Also, according to the given condition,
a+4x = 85100 = 1720
[∵ Out of 6 additional questions attempted, she got 2 wrong i.e., she got 4 more correct answers]
⇒ 20a + 80 = 17x ...(2)
From (1) and (2),
⇒ 15x + 80 = 17x
⇒ x = 40
∴ There are a total 40 questions in the exam.
Alternately, Because of 4 additional correct answers her marks increased by 10%.
⇒ 10% of total no. of questions = 4
⇒ total no. of questions = 4/10% = 40
Hence, option (c).
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