Question 635690
The age of a father was 6 times the age of his son two years ago.
 After six years the ratio of their ages was 10:3.
 what is the age of father now?
:
Let f = father's present age
let s = son's age
:
"The age of a father was 6 times the age of his son two years ago."
f - 2 = 6(s - 2)
f - 2 = 6s - 12
f = 6s - 12 + 2
f = 6s - 10
:
"After six years the ratio of their ages was 10:3."
{{{(f+6)/(s+6)}}} = {{{10/3}}}
cross multiply
10(s+6) = 3(f+6)
10s + 60 = 3f + 18
10s + 60 - 18 = 3f
10s + 42 = 3f
Replace f with (6s-10)
10s + 42 = 3(6s-10)
10s + 42 = 18s - 30
42 + 30 = 18s - 10s
72 = 8s
s = 72/8
s = 9 yrs is the son's age
then
f = 6s - 10
f = 6(9) - 10
f = 54 - 10
f = 44 yrs is the father's age
:
:
:
Confirm that
{{{(44+6)/(9+6)}}} = {{{50/15}}} = {{{10/3}}}