Question

The sum of ages of father and his son is 60 years . After 15 years , father will be twice as old as his son . Their present ages are :

Answer 1

Answer:

father x yrs

son=(6o-x)

After 15 yrs

father =x+15

son=60-x+15=75-x

x+15=2(75-x)

x+15=150-2x

3x = 150-15

3x = 135

x = 135/3=45

fatherx=45 yrs

son=60-x = 6o-45=15yrs

Answer 2

GIVEN

The Father's age + Son's age = 60

After 15yrs Father's age = 2 × Son's age

TO FIND

The age of Father and Son

SOLUTION

Let the age of the Father be x

and the age of the son be y.

According to the Given Question,

x + y = 60 ... eq.01

x + 15 = 2( y + 15) ...eq.02

Solving equation 01 and 02 by Linear Equation in Two variable we have :-

x + y = 60 => x = 60 - y ...eq.03

and

x + 15 = 2( y + 15)

x + 15 = 2y + 30

=> x - 2y = 15

Substituting value of x from eq.03

=> 60 - y - 2y = 15

=> 60 - 3y = 15

=> - 3y = - 45

=> y = 15yrs

Putting this value in equation 01 :-

x + y = 60

=> x + 15 = 60

=> x = 60 - 15

=> x = 45yrs

Hence the age of Father is 45yrs and age of son is 15yrs. (ANS)

VERIFICATION

Substituting both the values of L.H.S. and R.H.S. to check our solution in eq.02 :-

x + 15 = 2( y + 15)

=> 45 + 15 = 2 ( 15 + 15 )

=> 60 = 2 × 30

=> 60 = 60

=> LHS = RHS

Hence our Answer is correct.