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by sanaa.rizwan » Thu May 16, 2013 8:28 am
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated, creating trees that are part Fuji and part Gala. The number of his trees that are pure Fuji plus the number that are part Fuji and part Gala totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

a 22
b 33
c 55
d 77
e 88
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by mfindelhi » Thu May 16, 2013 9:07 am
sanaa.rizwan wrote:A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated, creating trees that are part Fuji and part Gala. The number of his trees that are pure Fuji plus the number that are part Fuji and part Gala totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

a 22
b 33
c 55
d 77
e 88
  1. Let total trees to be x
    10% tress cross pollinated -> 0.1x. This will be the number of half Gala, half Fuji tress.
    Number of pure Fuji tress -> 3x/4
Now it is also given that pure Fuji + cross pollinated = 187
Substituting values from 2 and 3
3x/4 + x/10 = 187
15x+2x = 187*20
x = 220

Pure Gala = 220 - 187 = 33 , hence, correct answer is B
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by Atekihcan » Thu May 16, 2013 10:10 am
Almost no calculation is required to solve this problem if we note that total number of trees must be multiple of 10 as 10% of total cross pollinated, which must be an integer.

So, (number of pure Fuji + number of pure Gala + number of part Fuji and part Gala) must be multiple of 10.
So, (187 + number of pure Gala) must be multiple of 10.
So, number of Gala must end with 3.

Answer : B
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