Question 62

A bartender initially serves the customer 60% concentrated alcohol. Every time the customer finishes 50% of the drink, the bartender refills it with a 20% solution up to the brim. After how many refills, will the alcohol concentration of the drink be less than 22%?

Thinking about the problem, when the bartender refills the drink, 50% of the glass is with current concentration, and the other 50% (the one being filled) is 20%, since both are equal in quantities, the resulting concentration would be the mid-point between the two concentrations, or the average of the two values.Β 

1st refill (20+60)/2 = 40%

2nd refuill (20+40)/2 = 30%

3rd refill (20+30)/2 = 25%

4th refill (20+25)/2 = 22.5%

5th refill (20+22.5)/2 = 21.25%

Hence, after the 5th refill, the concentration would be less than 22%

Therefore, Option D is the correct answer.Β 

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