Question

Sum of the ages of father and his daughter is 70 years. After 10 years father will be twice as old as his daughter. Find their present ages.​

Answer 1

Let their present ages be x

After 10 years

Fathers age =2×x+10

=2x+10

Daughter's age =x

Sum of their ages=70

Therefore the equation is

2x+10+x=70

Transpose 10 to RHS

2x+x=70-10

3x=60

Divide both sides by 3

3x/3=60/3

x=20

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Answer 2

Father's age = 50 years and daughter's age = 20 years

Given:

Sum of the ages of father and his daughter is 70 years

After 10 years father age will be twice as old as his daughter age.

To find:

Present ages of father and daughter

Solution:

Let x, and y be the ages of father and daughter

From given data  x + y = 70 ------(1)

After 10 years their ages will be

Father's age = x + 10  and daughter's age = y+10

After 10 years father age will be twice as old as his daughter age

⇒ x + 10 = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x - 2y = 10 -------(2)

Subtract (2) from (1)

⇒  x + y - (x -2y) = 70 - 10

⇒  x + y - x +2y = 60

⇒ 3y = 60

⇒ y = 20 years

Substitute y = 20 in (1)

⇒ x + 20 = 70

⇒ x = 50 years

Therefore,

Father's age = 50 years and daughter's age = 20 years.

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