Question 4

In a group of students, x number of students drink only Fruit Juice, 2x number of students drink only Coke. $$\frac{57}{x}$$ students drink both Fruit Juice and Coke and the students who drink neither Fruit Juice nor Coke are $$\frac{57}{3x}$$. The number of students who drink Coke may be

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No of persons who drink coke = 2x + 57/x

As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.

No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only

When x=1, no. of persons who drink coke = 2+57 = 59

When x=19, no. of persons who drink coke = 38 + 3 = 41

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