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Question:

Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90.Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?

Explanation:

Total exams given = x

Score of previous exams = y

$\frac{y + 97}{x} = 90$

$\frac{y + 70}{x} = 87$

$\frac{y}{x} + \frac{97}{x} =90$

$\frac{y}{x} + \frac{70}{x} = 87$

$\frac{y}{x} = 90 - \frac{97}{x}$

$\frac{y}{x} = 87 - \frac{70}{x}$

$∴ 90 - \frac{97}{x} = 87 - \frac{70}{x}$

$ 3 = \frac{- 70}{x} + \frac{97}{x} = \frac{27}{x}$

$ x = 9$

Hence, option (d).

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