A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence what is the present age of father?
Answers
Present age of father =3x
Present age of son = x
After fifteen years there ages will be 3x +15 and x +15
By the given condition
3x+15=2(x+15)
3x + 15 = 2x +30
X =15
Therefore present age of father = 3x = 3×15=45
Present age of son =x
=15
Let,
Present age of the son be a years
Present age of the father be 3a years
After 15 years, ages will be increased by 15 years : -
So, age of son after 15 years = present age + 15 years
⇒ Age of son after 15 years = a years + 15 years
⇒ Age of son after 15 years = ( a + 15 ) years
And, age of father after 15 years = present age + 15 years
⇒ Age of father after 15 years = 3a years + 15 years
⇒ Age of son father after 15 years ( 3a + 15 ) years.
According to the question, after 15 years age of father will be twice old as father's age.
∴ Age of father after 15 years = 2 x age of son after 15 years
⇒ 3a + 15 = 2( a + 15 )
⇒ 3a + 15 = 2a + 30
⇒ 3a - 2a = 30 - 15
⇒ a = 15
Therefore,
Present age of son = a years = 15 years
Present age of father = 3a years = 3( 15 ) years = 45 years