Question

A father is 7 times as old as his son. Three years
ago, the father was 13 times as old as his son.
What are their present ages?
monta
taining 50%​

Answer 1

Let the present age of the son be x and that to of his father which is 7 times =7x

Then, 2 years ago their ages :

(x-2) of son 

(7x-2)  of father

Given, 13(x−2)=7x−2

Then,

13x−26=7x−2

=13x−7x=26−2

6x=24

or x=4 and that of his father = 28 years

ageofson=x=4years

ageoffather=7x=28years

Answer 2

Given that , A father is 7 times as old as his son. Three years ago, the father was 13 times as old as his son.

Exigency To Find : Their [ Father and Son ] Present ages ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Present age of Father be x yrs .

Given that ,

⠀⠀⠀▪︎⠀A father is 7 times as old as his son.

Therefore,

• Present age of Father is 7x yrs .

⠀⠀⠀⠀⠀⠀⠀⠀☆ Before 3 years their ages :

• Age of Father will be ( 7x - 3 ) yrs .
• Age of Son will be ( x - 3 ) yrs .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\qquad \qquad \bigstar \:\:{\underline {\purple {\bf According \:\:To \:\:The\:\:Question \:\::\:}}}$

⠀⠀⠀⠀⠀━━━ Three years ago , the father was 13 times as old as his son.

$\qquad \dashrightarrow \sf \:\Big\{ Father's \:age\: \:_{( \:3 \:years \:ago \:)}\: \:\Big\}\:\:=\:13 \:\Big\{ Son's \:age\: \:_{( \:3 \:years \:ago \:)}\: \:\Big\}\:$

$\qquad \dashrightarrow \sf \:\Big\{ 7x - 3 \:\Big\}\:\:=\:13 \:\Big\{\:x - 3 \:\Big\}\\\\\:$

$\qquad \dashrightarrow \sf \:\Big\{ 7x - 3 \:\Big\}\:\:=\: \:\Big\{\:13x - 39 \:\Big\}\\\\\:$

$\qquad \dashrightarrow \sf \: 7x - 3 \:\:\:=\: \:\:13x - 39 \:\:$

$\qquad \dashrightarrow \sf \: 7x - 13 x \:\:\:=\: \:\: - 39 - 3 \:\:$

$\qquad \dashrightarrow \sf \: -6x \:\:\:=\: \:\: - 42 \:\:$

$\qquad \dashrightarrow \sf \: x \:\:\:=\: \:\: \dfrac{- 42}{-6} \:\:$

$\qquad \dashrightarrow \sf \: x \:\:\:=\: \:\: 7 \:\:$

$\qquad \dashrightarrow \underline {\boxed{\pmb{\frak{\purple { x \:=\: 7\:yrs \: }}}}}\:$

Therefore,

• Present age of Son is x = 7 yrs &
• Present age of Father is 7x = 7(7) = 49 yrs .

$\qquad \therefore \underline {\sf Hence, \:Present \:age \:\:of \: Father \:\:and \:Son \:are \:\pmb{\bf 7\:yrs \:\&\:49 \:yrs \: }\:, respectively.\:}$