Pick any two ratios and any two moments and the solver runs the shortcut: count the gaps, scale them to match, read the shift, price one unit. All four cases below describe the same mother and daughter — 70 and 30 today — from four different pairs of facts, so the scaling changes and the answer does not.
3 : 1 ten years ago, 2 : 1 ten years hence
Mother 70 · daughter 30 · gap 40
The last stat is the age gap, and it should read 40 for all four cases. To see a guard fire, put the further-from-1:1 ratio at the later moment — try 7 : 3 ten years ago against 5 : 1 in ten years.