Question

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

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that present age of father be 'x' years

and

Let assume that sum of present age of 2 children be 'y' years.

According to statement,

Father ‘s age is three times the sum of the ages of his two children.

$\bf :\longmapsto\:x = 3y - - - (1)$

Now, After 5 years,

Father age = x + 5 years

Sum of age of two children = y + 10 years.

According to statement,

After 5 years, his age will be twice the sum of the ages of two children.

$\rm :\longmapsto\:x + 5 = 2(y + 10)$

$\rm :\longmapsto\:3y + 5 = 2y + 20 \: \: \: \: \: \: \: \: \{ \because \: x \: = \: 3y \}$

$\rm :\longmapsto\:3y - 2y = 20 - 5$

$\rm :\longmapsto\:y = 15$

On substituting y = 15, in equation (1), we get

$\rm :\longmapsto\:x = 3 \times 15 = 45$

Hence,

• Present age of Father = 45 years.