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?

The son is 20 and the father is 80.

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