The current solution has #50# ml of bleach and a total volume of #50+950 = 1000# ml. If we add a certain quantity #b# of bleach, we will have more bleach, but also more solution in general: the ratio bleach-to-total volume will change as follows:

#\frac{50+b}{1000+b}#

we want this ratio to equal #15% = 0.15#, so we must ask

#\frac{50+b}{1000+b} = 0.15#

Solve for #b#: if we multiply both sides by #1000+b# we have

#50+b = 0.15(1000+b) = 150+0.15b#

Subtract #0.15b# from both sides:

#50+b-0.15b = 150#

Subtract #50# from both sides:

#b-0.15b = 150 - 50#

Simplify both sides:

#0.85b = 100#

Divide both sides by #0.85#

#b = \frac{100}{0.85} \approx 117.6#

Let's check our answer: the new solution will have #50+117.6 = 167.6# ml of bleach, for a total volume of #1000+117.6 = 1117.6# ml. The ratio is

#\frac{167.6}{1117.6} \approx 0.15#

so we're good!