Cross Pollination

[alivapriyada]

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. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88

[goyalsau]

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. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88

33 trees are pure Gala.

[klmehta03]

Assume the total number of trees is x
pure fuji trees is y
pure gala tress is z
cross pollinated is 0.1x
so first equation y+0.1x=187....(1)
second equation is y=0.75x....(2)
From 1) and 2) eqn
x=220 ; y=165
total trees y+z+0.1x=220
z= 33.
Hope this helps

[GMATGuruNY]

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. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88

Let c = cross pollinated, f = fuji, g=gala

c+f = 10% + 3/4 = 85%
So g = 15%
So (c+f):g = 85:15 = 17:3
c+f = 187
So 187/g = 17/3
g = (3*187)/17 = 33.

The correct answer is B.

[alivapriyada]

@All...thanks a lot!!!
got the doubt cleared.
ans is 33

[minkathebest]

I tried doing this using the double matrix method and got stuck until I figured out that there is a hidden constraint here. The Number of Non-Gala trees and Non-Fuji trees is 0. This makes the 33 easily. I did not have that as a zero first in my matrix for this problem and wondered what to do with it when I got 33.