Question

After 10 years, the father’s age will be 3 times the sum of the ages of his two children.

Answer 1

QUESTION

Father's age is 3 times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

SOLUTION

Let the age of father be x years and sum of the ages of his children by y years.

After 5 years,

$\bold{Father's \ age} = (x + 5) years \\\bold{Sum \ of \ ages \ of \ his \ children} = (y + 10) years$

Given

$x = 3y --(1)\\ x + 5 = 2(y + 10) x - 2y = 15 - - (2)$

Solving (1) and (2), we get,

$3y-2y=15$

$\implies y = 15$

$\boxed{\boxed{\bold{Therefore, \ the \ father \ is \ 45 \ years \ old}}}}$

                                                             

Answer 2

$\large{\underline{\underline{\bf{APPROPRIATE \:QUESTION:-}}}}$

Ques: Father's age is Three times the sum of ages of his two children. After 10 years, the father’s age will be twice the sum of the ages of his two children. Find the present ages of father and children.

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• Father's age is Three times the sum of ages of his two children
• After 10 years, the father’s age will be twice the sum of the ages of his two children.

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

Let the present ages of father and son be x years and y years respectively.

⁂ If father's age is Three times the sum of ages of his two children

$\implies$$\rm{ x = 3(y + y)}$

$\implies$$\rm{ x = 3 \times 2y}$

➣ $\large\bf\red{x = 6y....1)}$

⁂ After 10 years, the father’s age will be twice the sum of the ages of his two children

Ten years later , Father's age = (x + 10)years

Ten years later , Father's age = (y + 10)years

According to given conditions:-

$\implies$$\rm{(x + 10) = 2(y + 10)+(y+10)}$

$\implies$$\rm{(x + 10) = 2(2y + 20)}$

$\implies$$\rm{x + 10 = 4y + 40}$

$\implies$$\rm{x -4y = 40-10}$

➢ $\large\bf\red{x -4y = 30...2)}$

☞ Putting the value of x in equation 2),we get

$\implies$$\large\rm{x -4y = 30}$

$\implies$$\rm{6y -4y = 30}$

$\implies$$\rm{2y = 30}$

➜ $\rm{ y =\cancel\dfrac{30}{2}}$

✯ $\large\bf\red{y = 15}$

☞ Putting the value of y in equation 1),we get

$\implies$$\large\bf{x = 6 \times 15}$

✯ $\large\bf\red{x = 90}$

Thus, the present age of father is 90 years and children is 15 years

$\large{\underline{\underline{\bf{FINAL\:ANSWER:-}}}}$

$\large{\boxed{\boxed{\bf{\red{Father's\: age = 90\: years}}}}}$

$\large{\boxed{\boxed{\bf{\red{Children's \:age = 15\: years }}}}}$