Question

Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of his son. Find the present ages of father & son.

Answer 1

Let the age of father is x years and that of son is y years.
Then by the given question,
x-2=5(y-2)
or, x-5y=-10+2
or, x-5y=-8
or, x=5y-8
x+2=3(y+2)+8
or, x-3y=6+8-2
or, 5y-8-3y=12
or, 2y=12+8
or, y=20/2
or, y=10
then x=5y-8=50-8=42
Then, the age of father is 42 yrs. and the age of sun is 10 yrs.

Answer 2

Answer:

Step-by-step explanation:

let f = father's present age

let s = son's age

:

Write an equation for each statement, simplify as much as possible.

:

" two years ago , a father was five times old as his son ."

f - 2 = 5(s-2)

f - 2 = 5s - 10

f = 5s - 10 + 2

f = 5s - 8

"two years later from today his age will be 8 years more than three times the age of his son "

f + 2 = 3(s+2) + 8

f + 2 = 3s + 6 + 8

f = 3s + 14 - 2

f = 3s + 12

replace f with (5s-8), from the 1st statement

5s - 8 = 3s + 12

5s - 3s = 12 + 8

2s = 20

s = 10 yrs is the son's age

then

f = 5(10) - 8

f = 42 yrs is father's age

:

you can confirm this by putting these ages in both original statements and see if they are true.