A man is four times as old as his son. 10 years later, the man will be three times as old as his son. What is the man's current age?

now:

Son is 20 years old

Father is 80 years old

10 years later:

Son will be 20+10 = 30 years old

Father will be 80+10=90

Step-by-step explanation:

Solution:

Let

Son's age = x years

Father's age = y years

At Present:

Age relation between Father and Son:

y = 4x ... 1

After 10 year:

Father's age = y+10

Son's age = x+10

New Age relationship between Father and Son:

y + 10 = 3 (x + 10) ... 2

Solving eq 2 by putting the value of y from eq 1.

4x + 10 = 3 (x + 10)

4x + 10 = 3x + 30

4x - 3x = 30 - 10

x = 20

Put the value of x=20 in eq 1

y = 4*20 = 80

At present:

Son is 20 years old

Father is 80 years old

Age relationship: 20:80 = > 1:4

After 10 years:

Son will be 20+10 = 30 years old

Father will be 80+10=90

Age relationship: 30:90 = > 1:3

The son is 20 and the father is 80.