Question

A father's age in three times the sum of the ages of his two children. After 5 years his age will b
two times the sum of their ages. Find the present age of the father.
​

Answer 1

Answer

$\boxed{\boxed{\mathsf{Age\: of\: father = 45yrs}}}$

Step-by-step Explanation :

Given

• A father's age is three times the sum of the ages of his two childrens.

• After 5 years his age will be 2times sum of his children's age

To find

• Present age of father

Solution

Now let,

Present age of father be = f

Present age of First child be = x

and

Present age of Second child be = y

Now According To Question

Present age of father = 3 times sum of ages of children

That is,

$\implies \textsf{Present age of father = 3(x + y)}$

$\implies \textsf{f = 3(x + y)}$ ------- (1)

*Now after 5 years his age will be twice the sum of his children's age

Thus here,

$\implies \textsf{Age of father after 5yrs = f + 5}$

$\implies \textsf{Age of first child after 5yrs = x+ 5}$

$\implies \textsf{Age of second child after 5yrs = y + 5}$

Therefore According to Question we have

$\longrightarrow \: \mathsf{f + 5 = 2(x + 5 + y + 5)}$

$\longrightarrow \: \mathsf{f + 5 = 2(x + y + 10)}$ ------ (2)

Now let us Take

Sum of ages of children = x + y = b

Therefore we have EQ (1)

$\implies \textsf{f = 3(b)}$

$\implies \textsf{f = 3b}$

And Equation 2 we have

$\longrightarrow \: \mathsf{f + 5 = 2(x + y + 10)}$

$\longrightarrow \: \mathsf{f + 5 = 2(b + 10)}$

$\longrightarrow \: \mathsf{f + 5 = 2b + 20}$

Now subtracting Equation 1 from 2 we have

$\longrightarrow \: \mathsf{f + 5 - f = 2b + 20 - 3b}$

$\longrightarrow \: \mathsf{5 = -b + 20}$

$\longrightarrow \: \mathsf{-15 = -b}$

$\longrightarrow \: \mathsf{b = 15}$

Now putting value of b in equation 1 we have

$\implies \textsf{f = 3b}$

$\implies \textsf{f = 3(15)}$

$\implies \textsf{f = 45}$

Therefore we have

$\longrightarrow \: \textsf{Present age of father = f = 45yrs}$

Thus Required answer :

$\underline{\boxed{\mathsf{Age\: of\: father = 45yrs}}}$

Answer 2

★Given :----

• Father present age = 3×(two children)
• After 5 years Father age = 2(two children)

★To Find :----

• Present Age of Father ?

★Solution::::-------------

The main logic of question is that, After 5 years we have to add 5 in father age , but since children are two , we have to add 5 two times ..

Let Father Present age = x years .

Both children Total present age = y years .

A/q,

x = 3y ------------------- Equation (1)

Now,

After 5 years father will be = (x+5) years .

Both children total will be = (y+10) years [ Told above the reason. ]

A/q,

(x+5) = 2(y+10) ------------------- Equation (2)

➾ (x+5) = 2y + 20

➾ x - 2y = 15

Putting value of Equation (1) Now we get,,

➾ 3y - 2y = 15

➾ y = 15 = children Total present age .

⛬ Father present age is = 3y = 3×15 = $\boxed{\boxed{\mathsf{45years}}}$

(Hope it Helps you)