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

Answer:

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