Question

Two years ago, father was three times as old as his son and two years hence, twice will be equal to five times that of his son. Find their present ages. his age ​

Answer 1

Given is the relationship of ages of a father and son over two years, Find their current ages.

Explanation:

• Let the current age of the father be denoted 'F' and the age of his son be denoted by 'S'.  
• Then we are given that twice the age of the father is equal to five times the age of the son, $2F=5S$     ---(a)  
• Now two years ago both 'F' and 'S' would be reduced by two. $->F-2,\ S-2$
• Hence, two years ago father's age was three times that of the son's, $F-2=3(S-2)$  ---(b)
• Equating (a) in (b) we get the required current ages,  
• $\frac{5S}{2}-2=3(S-2)\\ ->5S-4=6S-12\\->S=8\ yrs\\->F=\frac{5S}{2}\\ ->F=20\ yrs$    
• Hence, the current ages of the father and the son are $20$ and $8$ years respectively.

Answer 2

Given,

Two years ago, father was three times as old as his son and two years hencethe  twice will be equal to five times that of his son.

To find,

their present ages.

Solution,

Let the father's age be x and the son's age be y

Situation 1 :- 2x = 5y ---- (a)

Situation 2 :- x - 2 = 3(y - 2) ----- (b)

Equating both

5y/2 - 2 = 3(y - 2)

5y - 4 = 2(3y - 6)

5y - 4 = 6y - 12

12 - 4 = 6y - 5y

8 = y

Age of the father = 5y/2

= 5(8)/2

= 40/2

= 20

Thus, the age of the father is 20yrs and the age of the son is 8yrs old right now