Question

you need to use 3 solutions of drug H containing respectively 50%, 20% and 5% to make 600ml of 10% drug H. How much of the 50% will you use?

Answer 1

try 400 ml of 5% and 200 ml of 20% for example then you need NONE of the 50%.
Unless you have another criterion, the problem has many solutions.

Answer 2

If the amounts of the three solutions are x,y,z, respectively, then all you have given is

x+y+z = 600
.50x + .20y + .05z = .10*600

There are many solutions (as it were), such as

5% 20% 50%
400 200 0
440 140 60
500 50 50
520 20 60
533 0 67