Five years ago, a grandfather was 7.5 times older than his grandson. After 15 years from today, the grandfather will be 20/7 times as old as his grandson will be at that time. What was the ratio of the ages of grandfather and grandson 1 year ago?

Let 5 years ago, grandson's age be x years and grandfather's age be 7.5x years. Now, after 15 years, grandson's age = x + 5 + 15 = x + 20 years and grandfather's age = 7.5x + 5 + 15 = 7.5x + 20 years Now, according to question, 20(x + 20)/7 = 7.5x + 20 x = 8 So, the present age of grandson = 8 + 5 = 13 years and that of the grandfather = 7.5 x 8 + 5 = 65 years One year ago, grandfather's age = 65 - 1 = 64 years and grandson's age = 13 - 1 = 12 years Now, ratio of their ages 1 year ago = 64 : 12 = 16 : 3