Four years ago a man was 6 times as old as his son. after 16 years he will be twice as old as his son. what is the present age of man and his son? 34, 9 33, 7 35, 5 36, 6

General
1

four years ago a man was 6 times as old as his son. after 16 years he will be twice as old as his son. what is the present age of man and his son? 34, 9 33, 7 35, 5 36, 6

2

Four years ago a man was 6 times as old as his son. After 16 years, he will be twice as old as his son. What is the present age of the man and his son?

Answer:
Let’s denote the present age of the man as m and the present age of the son as s.

According to the first statement, four years ago, the man was 6 times as old as his son:
[ m - 4 = 6(s - 4) ]

According to the second statement, after 16 years, the man will be twice as old as his son:
[ m + 16 = 2(s + 16) ]

Now, we have two equations:

  1. ( m - 4 = 6s - 24 )
  2. ( m + 16 = 2s + 32 )

Let’s solve these equations to find the present age of the man and his son:

From equation 1:
[ m = 6s - 20 ]

Substitute this into equation 2:
[ 6s - 20 + 16 = 2s + 32 ]
[ 6s - 4 = 2s + 32 ]
[ 4s = 36 ]
[ s = 9 ]

Now, substitute s=9 back into m = 6s - 20:
[ m = 6(9) - 20 ]
[ m = 54 - 20 ]
[ m = 34 ]

Therefore, the present age of the man is 34 years and the present age of his son is 9 years. So, the correct answer is 34, 9.