##x=25g##

The initial mass of the solution was 100g As 50% (w/w) was present in 100g solution , we can say the mass of the solute in initial solution was 50g

After addition of x g solute in 100g solution the changed mass of solution became (x+100)g and total amount of solute became (x+50)g. So the percentage of solute in final solution became 60%.

So

##(x+50)/(x+100)xx100=60##

##=>(x+50)/(x+100)=60/100=0.6##

##=>x+50=0.6(x+100)##

##=>x+50=0.6x+60##

##=>x-0.6x=60-50##

##=>0.4x=10##

##=>x=10/0.4=25##