Question

A father is 6 times older than his son. After 4 years, he will be only 4 times as old as his son. What are their present ages?

Answer 1

Given :

• Father is 6 times older than his son.
• After 4 years, father's age will be 4 times as old as son's age.

To Find :

• Present age of Father
• Present age of Son

Solution :

Let the present age of father be x years.

Let the present age of son be y years.

Case 1 :

The age of Father, x is 6 times the age of son, y.

Equation :

$\longrightarrow$ $\sf{x=6y}$

$\sf{x-6y=0\:\:\:\:(1)}$

Case 2 :

After 4 years, father's age, x will be 4 times the age of son.

Age of father after 4 year, (x+4) years.

Age of son after 4 year, (y+4) years.

Equation :

$\longrightarrow$ $\sf{(x+4)=4(y+4)}$

$\longrightarrow$ $\sf{x+4=4y+16}$

$\longrightarrow$ $\sf{x-4y=16-4}$

$\longrightarrow$ $\sf{x-4y=12\:\:\:(2)}$

Now, subtract equation (1) from (2),

$\longrightarrow$$\sf{x-6y-(x-4y) =0-12}$

$\longrightarrow$ $\sf{x-6y+x+4y=-12}$

$\longrightarrow$ $\sf{-6y+4y=-12}$

$\longrightarrow$ $\sf{-2y=-12}$

$\longrightarrow$ $\sf{y=\dfrac{-12}{-2}}$

$\longrightarrow$ $\sf{y=\dfrac{12}{2}}$

$\longrightarrow$ $\sf{y=6}$

Substitute, y = 6 in equation (1),

$\longrightarrow$ $\sf{x-6y=0}$

$\longrightarrow$ $\sf{x-6(6)=0}$

$\longrightarrow$ $\sf{x-36=0}$

$\longrightarrow$ $\sf{x=36}$

$\large{\boxed{\bold{\purple{Present\:age\:of\:father\:=\:x\:=\:36\:years}}}}$

$\large{\boxed{\bold{\purple{Present\:age\:of\:son\:=\:y\:=\:6\:years}}}}$

Answer 2

$\huge{\orange{\fbox{\green{\fbox{\mathcal{\orange{An}\blue{sw}\green{er}}}}}}}$

$\large{\orange{\fbox{\green{\fbox{\mathcal{\orange{No}\green{te}}}}}}}$

• $\orange{Given\;Atpresent\;Dad\;age=6(Son's\;age)}$

• $\blue{Let\;son\;age=x\;and\;dads\;age=y}$

• $\green{y=6x-----(1)}$

• $\orange{Given\;After\;4\;years\;Dad\;age=4(Son's\;age)}$

• $\blue{y+4=4(x+4)}$

• $\blue{y+4=4x+16----(2)}$

• $\green{put\;(1)\;in\;(2)}$

• $\orange{6x+4=4x+16}$

• $\blue{x=6\;and\;y=36}$

$\large{\red{\fbox{\green{Present\;age\;of\;dad=36years\;and\;son=6years}}}}$