10 years ago daughter’s age was two-fifth of her mother’s age that time. While 10 years hence her age will be three-fifth of her mother’s age then. Find the difference in the ages of the two.

Let daughter's and mother's current ages be d and m. 10 years ago: d-10 = 2/5(m-10) → 5d-50 = 2m-20 → 5d-2m = 30. 10 years hence: d+10 = 3/5(m+10) → 5d+50 = 3m+30 → 3m-5d = 20. Solving: Adding gives m = 50, then d = 26. Age difference = 50-26 = 24. This linear equations problem requires setting up relationships at different time points.