Question

the age of a father is equal to sum of the ages of his 6 children. After 15 years twice the age of the father will be the sum of ages of his children. Find the age of the father

Answer 1

Let the age of father be X and let the ages of his 6 children be Y1, Y2, Y3, Y4, Y5 and Y6
now,
X=Y1+Y2+Y3+Y4+Y5+Y6--(i)

after 15 years,
2(X+15)= (Y1+Y2+Y3+Y4+Y5+Y6)+(15×6)

2X+30=X+90 [from (i)]
2X-X=90-30
X=60
therefore age of father is 60 years

Answer 2

Answer:

The age of the father is 60 years.

Solution:

Let the present age of the father be x years.

Let the present ages of his six children be a₁, a₂, a₃, a₄, a₅, and a₆ years respectively.

Given that age of father = sum of ages of his 6 children

x = a₁ + a₂ + a₃ + a₄ + a₅ + a₆   ------------------- (i)

Now, after 15 years

Age of the father = (x + 5) years

Ages of his 6 children = (a₁ + 15), (a₂ + 15), (a₃ + 15), (a₄ + 15), (a₅ + 15), and (a₆ + 15) years

In the question, it is given that after 15 years twice the age of the father will be the sum of ages of his children.

2(x + 15) = (a₁ + 15) + (a₂ + 15) + (a₃ + 15) + (a₄ + 15) + (a₅ + 15) + (a₆ + 15)

2x + 2(15) = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + 15 + 15 + 15 + 15 + 15 + 15

2x + 30 = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + 90

2x = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + 90 - 30

2x = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + 60

But from (i), a₁ + a₂ + a₃ + a₄ + a₅ + a₆ = x

∴ 2x = x + 60

2x - x = 60

x = 60 years

Hence, the age of the father is x = 60 years.

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