Question

Father's age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Answer 1

Let the present age of father be x years and the present ages of his two children’s be y and zyears.

The present age of father is three times the sum of the ages of the two children’s. Thus, we have

${\displaystyle x=3(y+2)}$

${\displaystyle \Rightarrow y+z=\frac{x}{5}}$

After 5 years, father’s age will be (x+5) years and the children’s age will be (y+5) and (z+5) years. Thus using the given information, we have

${\displaystyle x+5=2\{(y+5)+(z+5)\}}$

${\displaystyle \Rightarrow x+5=2(y+5+z+5)}$

${\displaystyle \Rightarrow x=2(y+z)+20-5}$

${\displaystyle \Rightarrow x=2(y+z)+15}$

So, we have two equations

${\displaystyle y+z=\frac{x}{3}}$

${\displaystyle x=2(y+z)+15}$

Here x, y and z are unknowns. We have to find the value of x.

Substituting the value of (y+z) from the first equation in the second equation, we have

By using cross-multiplication, we have

${\displaystyle x=\frac{2x}{3}+15}$

${\displaystyle \Rightarrow x=\frac{2x}{3}=15}$

${\displaystyle \Rightarrow x(1-\frac{2}{3})=15}$

${\displaystyle \Rightarrow \frac{x}{3}=15}$

${\displaystyle \Rightarrow x=15\times 3}$

${\displaystyle \Rightarrow x=45}$

Hence, the present age of father is 45 years.