Let f,g,h represent areas of shapes F,G,H. Since we only care about proportions set f=1. We know g+h= 6/10. We get one more equation g/5 + h/3 = 1/7 by assuming overlap regions match shaded regions. This is implied by the drawing rather than explicitly stated but without it the problem is not solvable. Solving gives g= 15/35, h= 6/35, and shaded fraction of whole figure is 5/51.