Question

fathers age is equal to the sum of the ages of his three children.
in 9 years his age will be equal to the sum of the two eldest sons amd three years after that his age will be equal to the sum of his eldest and youngest children.
again 3 yeras after that his age will be3 equal to the sum of the ages of his two youngest children.
find fathers present age?

Answer 1

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Answer 2

Concept:

If the present age is y, then n times the present age = ny.

If the present age is x, then age n years later/hence = x + n.

If the present age is x, then age n years ago = x – n.

The ages in a ratio a: b will be ax and bx.

Given:

Father's age is equal to the sum of the ages of his three children.

To find:

Father's present age.

Solution:

Let the father’s age be a year and that of his oldest, younger, and youngest children be x years,y years, and z years respectively.

According to the problem,

as everyone's age grew over time,

a =x+y+z in the present year;.......(1)

a+9 = (x+9)+(y+9) after 9 years;

or, a = x+y+9..........(2)

a+9+3  =(x+9+3)+(z+9+3) after (9+3) years;

or, a = x+z+12...............................(3)

and a+9+3+3 = y+z after (9+3+3) years;

or, a = y+z+15...............................(4)

Putting the value of (2) in (1) we get

z = 9 years.

Putting the value of (3) in (1) we get

y = 12 years.

Putting the value of (4) in (1) we get

x = 15 years.

Putting all the ages of the children in (1) we get

a = 36 years

∴ Father's age is 36 years.

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