Answer:
The Amount of 80% solution of Apple juice = 60 liters
The Amount of 30% solution of Apple juice = 40 liters
Step-by-step explanation:
Given in the question as : 
 A cafeteria worker need to make 100 liters of  of 50% solution of apple juice 
Let for 80% solution of apple juice he need x liter 
And for 30% solution of apple juice he need y liter 
I,e x + y = 100 
And 80% of x + 30% of y = 50% of (x + y)
Or 80% of x + 30% of y    = 50% of x + 50 % of y
I.e (80% of x - 50% of x) = ( 50 % of y - 30% of y)
Or, 30% of x = 20% of y
∴  3 x = 2 y
Or,  x = y
 y
∵  x + y = 100 ,
So ,  y + y = 100
 y + y = 100
Or,   = 100
 = 100
∴   5y = 200
i.e y =  = 40 liters
 = 40 liters
And x = 100 - 40 = 60 liters
Hence , The Amount of 80% solution of Apple juice = 60 liters
And        The Amount of 30% solution of Apple juice = 40 liters    Answer