6 years ago the average of husband and wife was 20 years. Today the average age of husband, wife and child is 20 years. How old is the child?

8 years

6 years ago, 

Average age of husband and wife is = 20 years 

Sum of ages of husband and wife = 20 × 2 = 40 years

Sum of  present ages of husband and wife = 40 + 12 = 52 years

At present , the average age of husband , wife and child = 20 years 

Sum of  present ages of husband, wife and child = 20 × 3 = 60 years 

Age of child= 60 - 52 = 8 years