Solution X is 15% salt and the rest is water. Solution Y is 8% salt and the rest is water. How many litres of solution X need to be added to 5 litres of solution Y to make a solution that is 10% salt?

In 5 litres of solution Y you have 5*8%=0.4 litres of salt, and the rest 4.96 litres of water.
Now you add t litres of solution X (t to be determined). This contains t*15% litres of salt, and t*85% of water.

The total (t litres of solution X plus 5 litres of solution Y) contain t*15%+0.4 litres of salt, and you want it being 10%. Thus solve
\frac{15}{100}t+0.4=\frac{10}{100}(t+5).