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5/6:x::5/9:4/5

we know that - product of extreme=product of mean

ie. 5/6x4/5=Xx5/9

6/4=5X/9

6/4x9=5X

54/4=5X

54/20=X

5/6:x::5/9:4/5

Rearrange the above equation simply as:

5/6x = 5/9 x 5/4

5/6 x = 25/36      ------------------------(I)

from equation(I) determine the value of  'x' using cross multiplication

x= 36x5/25x6

x= 6/5

5/6x = 25/36

6x x 25=  5 x36

X= 5x36/25 x 6

X= 6/5 Ans

X=5/6

6/5

Lets start solving the question:

a:b=c:d

i.e a/b=c/d

using this formula

5/6:x= 5/9:4/5

x*(5/9)=(5/6)*(4/5)

x*(5/9)=4/6

x*(5/9)=2/3

both sides multiplying by 9/5

x=(2/3)*(9/5)

x=6/5

6/5