Question
A bag contains a certain number of fruits of three
varieties: apple, orange, and banana. The total number of apples and oranges is 13, which is 5 more than the number of apples in the bag. If two fruits are drawn at random without replacement, the probability that the first fruit drawn is an apple and the second is a banana is 14/95. Find the total number of fruits in the bag.Solution
Number of apple = 13 – 5 = 8 Number of orange = 5 Number of banana = x 14/95 = 8/(13 + x) * x/(12 + x) 380x = 7 * (13 + x) * (12 + x) 380x = 7 * (156 + 13x + 12x + x2) 7x2 – 205x + 1092 = 0 7x2 – 49x – 156x + 1092 = 0 7x(x – 7) – 156(x – 7) = 0 x = 7, 22.28(not possible) Required total = 13 + 7 = 20
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