Five years ago, the sum of Alwyn's age and his father's age was a third of five times the average of present ages of Alwyn and his father. If Alwyn will be 15 years old in 5 years from now how old is Alwyn's father now?
Answers
Alwyn's father is now 50 years old.
• Given,
Alwyn's age in 5 years from now = 15 years
=> Present age of Alwyn = (15 - 5) years = 10 years
• Let the present age of Alwyn's father be x years.
• The average of the present ages of Alwyn and his father = (10 + x) years / 2
5 times the average of their present ages = 5 { (10 + x) years / 2 }
• Age of Alwyn 5 years ago was (10 - 5) years = 5 years
Age of Alwyn's father 5 years ago was (x - 5) years.
Sum of their ages 5 years ago = { 5 + (x - 5) } years
• According to the question,
5 + (x - 5) = (1 / 3) of 5 { (10 + x) / 2 }
=> 5 + x - 5 = (1 / 3) × 5 { (10 + x) / 2 }
=> x + 5 - 5 = { 1 × 5 (10 + x) } / ( 3 × 2)
=> x + 0 = 5 (10 + x) / ( 3 × 2 )
=> x = (5 × 10) + (5 × x) } / 6
=> x = (50 + 5x) / 6
On cross-multiplying, we get,
x × 6 = 50 + 5x
=> 6x = 50 + 5x
=> 6x - 5x = 50
=> x = 50
Therefore, the present age of Alwyn's father is 50 years.