\(x(x-2)+x+2x+8+10=60\\ x^2-2x+3x+18=60\\ x^2+x-42=0\\ (x-6)(x+7)=0\\ \text{x has to be positive so it is 6}\)
Number that are british is x+2x+8 = 3x+8 = 18+8 = 26
\(P(british)=\dfrac{26}{60}=\dfrac{13}{30}\)
EDIT: Sorry this is not right
I overlooked the fact that the painting must be from the 20th century (T) to start with.
There are 30 in from the 20th century
6 of those are british
P( that it is british given that it IS from the 20th century) = 6/30 = 0.2