"I am seven times as old as you were when i was as old as you are" , said a man to his son. Find their present ages.if the sum of their ages is 110 years?

Question

anonymous · Answer

Let their ages be x and y

The sum is 110

so
x+y=110

anonymous · Answer

ok then?

anonymous · Answer

that's not right

mathstudent55 · Answer

Let the present father's age be f.
Let the present son's age be s.

f + s = 110

When the father was as old as the son is now, it was f - s years ago.
The son was then s - (f - s) = s - f + s = 2s - f years old

f = 7(2s - f)
f = 14s - 7f
8f = 14s
f = (14/8) s

f + s = 110
(14/8)s + s  = 110
s = 40

f = 70

The father is 70 and the son is 40.
30 years ago, the father was 40 and the son was 10.
The father is now 7 times older than when the son was 10, which is when the father was the son's current age of 40.

anonymous · Answer

ok i got it..thnxs

mathstudent55 · Answer

The son is s years old now, and the father is f years old now.
When the father was the age the son is now, that was f - s years ago..

                  Ages Now          Old Time was         Ages in the Past
Father               f                 f - s years ago          f - (f - s)
Son                   s                 f - s years ago         s - (f - s)

"I am seven times as old as you were when i was as old as you are" 

"I am" means the father's age now, f.
"seven times as old" means 7 *
" as you were " that means s - (f - s)
"when i was as old as you are" 

This translates into the equation
f = 7[s - (f - s)]
Which can be simplified to
f = 7(s - f + s)
f = 7(2s - f)
f = 14s - 7f