Grandfather is 15 time the age of his grandson today, in 10 years the grandson will be 3/17 the age of the grandfather. How old are the grandfather and grandson?

Grandfather is 15 time the age of his grandson today, in 10 years the grandson will be 3/17 the age of the grandfather. How old are the grandfather and grandson?

1 Answer
Apr 19, 2016

Today Grandfather is 75 years old, Grandson is 5 years old.

Explanation:

Let GF and GS be the current ages in years of the Grandfather and Grandson respectively

We are told that Grandfather is 15 times the age of the Grandson today

Therefore: GF = 15GS (1)

We are also told that in 10 years the Grandson will be 3/17 the age of the Grandfather.

Therefore: 3/17(GF+10) = GS+10 (2)

Substituting (1) in (2)

3/17(15GS + 10) = GS+10

45GS+30 = 17GS+170

28GS = 140

GS=140/28 = 5 Years

Substituting for GS in (1)

GF= 15 * 5 = 75 Years