You use the idea that

#"concentration=amount of substance/volume of solution"#

In symbols:

#c=n/v#

This means that

#n=cxxv#

In questions like this the total amount of substance does not change so we can write:

#(60xxV_(60))+(15xxV_(15))=30xx650" "color(red)((1))#

We also know that the total volume is #650"ml"# so we can also write:

#V_(60)+V_(15)=650" "color(red)((2))#

So we have set up two simultaneous equations. There are two equations and two unknowns so they can be solved easily.

From #color(red)((2))# we can rearrange:

#V_(60)=(650-V_(15))#

We now substitute this expression for #V_(60)# into #color(red)((1))rArr#

#60(650-V_(15))+15V_(15)=19500#

#:.39000-60V_(15)+15V_(15)=19500#

#:.39000-45V_(15)=19500#

#:.45V_(15)=39000-19500=19500#

#:.V_(15)=19500/45=433.3"ml"#

From #color(red)((2))# we know that:

#V_(60)+V_(15)=650#

#:.V_(60)=650-V_(15)#

#:.V_(60)=650-433.3=216.6"ml"#