PS 1

let total no. of trees be x

10%x = cross pollination

combined fuji = 187

pure fuji = 3x/4

only fuji = combined fuji - cross pollination

3x/4 = 187 - x/10

x = 220

pure fuji = 220*3/4 = 165

total = pure F + pure G + 22[both cross pollination]

220 = 165 + G +22

220 - 187 = G

33 = G

Hope this helps.

Pure fuji = 3/4 of total
cross-pollinated = 1/10 of total

together they are 3/4+1/10=15/20+2/20=17/20

so pure gala = 3/20 of total

set up the ratio:
187/17=?/3
?=33

(the ratio above says: if 17 parts mean 187 then 3 parts mean how many? while setting up such ratios, all you have to do is put corresponding items in similar places. eg. we could also write 3/17 = ?/187. here the ratio says: what number has the same multiplicative relationship with 187 as 3 has with 17)

@ parallel_chase
I am little confused by the wording
doesn't
while 3/4 of all his trees are pure Fuji
means 3/4th of 90% of x ??? as 10% seeds were pollinated ?

amitabhprasad wrote:@ parallel_chase
I am little confused by the wording
doesn't
while 3/4 of all his trees are pure Fuji
means 3/4th of 90% of x ??? as 10% seeds were pollinated ?

10%x = pollinated

90%x = pure G + pure F

we know that x=220

198 = G + 165 [pure F = total F - 10% polinated] or [3/4*220]

x = 198-165 = 33


Hope its clear.

Here is another way:

Let F = pure Fuji,
G = pure Gala
FG = crosspollinated.

T = F + G +FG ---------------(0)

We are given
F + FG = 187. -----------------(1)
F = 3/4 of total ==> 3T/4 -----------(2)

FG = 1/10 of Total -----------------(3)

So 3T/4 + T/4 = 187
Solving, T = 220.

Now back substituting T = 220 in (0)

220 = G + 187
So G = 33

HT Helps.