Haven't seen one like this before.....!!!
Since AB : BD = 1 : 5 so...from A to D there are 1 + 5 = 6 parts
And since AC : CD = 7 : 11 and we can divide each 6th part into 7 + 11 = 18 more parts
So.....from A to D there are 6 * 18 = 108 equal parts
So AB = [108 / 6] * 1 = 18 units
And BD = [108 / 6] * 5 = 90 units
And AC = [ 108/ 18] * 7 = 42 units
And CD = [ 108 / 18] * 11 = 66 units
AB = 18
BC = AC - AB = 42 - 18 = 24 units
CD = 66 units
A B C D
18 + 24 + 66 = 108
So AB : BC : CD = 18 : 24 : 66 = 3 : 4 : 11