A quantity of grey paint has a mass of $12 \mathrm{~kg}$. The grey paint is a mixture of black paint and white paint, of which $80 \%$ by mass is white paint. More white paint is added until the mixture is $90 \%$ white paint by mass. What is the resulting total mass of the paint, in $\mathrm{kg}$ ?
Since the grey paint has mass $12 \mathrm{~kg}$ and is $80 \%$ white paint, then the amount of white paint is $0.8 \times 12=9.6 \mathrm{~kg}$ and so the amount of black paint is $12-9.6=2.4 \mathrm{~kg}$.

For the new mixture to be $90 \%$ white paint and $10 \%$ black paint, the mass of white paint should be 9 times the mass of black paint, or $9 \times 2.4=21.6 \mathrm{~kg}$.

In total, the new mixture has mass $2.4+21.6=24 \mathrm{~kg}$.

ANSWER: 24