Question

At present the age of the father is 6 times the age of the son. If the age of the father after 6 years is the son Age is 3 times, but how old is the father now?​

Answer 1

Answer:

Let us start by the standard assumptions to solve such kind of sums,

Let the father’s age be y;

Let the son’s age be x;

So from the first condition: y=6x" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">y=6xy=6x

After 6 years, the father’s and son’s age will be : y+6 & x+6 years respectively.

Therefore, from the second condition: y+6=3(x+6)" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">y+6=3(x+6)y+6=3(x+6)

Substituting y as 6x in above equation we get,

6x+6 = 3x+18 ……………………………. on opening the brackets

3x = 12 or x = 4

Therefore, y = 6x = 6 x 4 = 24

Hence, the father’s age is 24 years and son’s age is 4 years.

Answer 2

Answer:

$\sf{The \ ages \ of \ father \ and \ son \ are}$

$\sf{24 \ years \ and \ 4 \ years \ respectively.}$

Given:

$\sf{\leadsto{At \ present \ the \ age \ of \ the \ father}}$

$\sf{is \ 6 \ times \ the \ age \ of \ the \ son.}$

$\sf{\leadsto{The \ age \ of \ the \ father \ after}}$

$\sf{6 \ years \ is \ times \ the \ son's \ age.}$

To find:

$\sf{Present \ ages \ of \ father \ and \ son.}$

Solution:

$\sf{Let \ the \ age \ of \ the \ father \ be \ x \ and}$

$\sf{the \ age \ of \ the \ son \ be \ y.}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{x=6y}$

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

$\sf{According \ to \ the \ second \ condition}$

$\sf{(x+6)=3(y+6)}$

$\sf{\therefore{x+6=3y=18}}$

$\sf{\therefore{x-3y=12...(2)}}$

$\sf{Subtract \ equation (1) \ from \ equation (2),}$

$\sf{we \ get}$

$\sf{x-3y=12}$

$\sf{-}$

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

________________

$\sf{3y=12}$

$\sf{\therefore{y=\dfrac{12}{3}}}$

$\boxed{\sf{\therefore{y=4}}}$

$\sf{Substitute \ y=4 \ in \ equation (1), \ we \ get}$

$\sf{x+6(4)=0}$

$\boxed{\sf{\therefore{x=24}}}$

$\sf\purple{\tt{\therefore{The \ ages \ of \ father \ and \ son \ are}}}$

$\sf\purple{\tt{24 \ years \ and \ 4 \ years \ respectively.}}$