Question

the fathers present age is equal to squere of his sons present age. of one year ago his age is 8 time his sons age. fins sons present age?

Answer 1

Answer:

let present age of son is x year

so, present age of father is x^2 year

one year ago , age of son (x-1) year

one year ago ,age of father (x^2-1)

according to question,

(x^2-1)=8(x-1)

=> x^2-1=8x-8

=> x^2-1-8x+8=0

=> x^2-8x+7=0

=> x^2-7x-x+7=0

=> x(x-7)-1(x-7)=0

=> (x-7)(x-1)=0

=> x-7=0

=> x=7

x-1

=> x=1

here x=7 because if x=1 then one year ago son is zero years old which is impossible.

so , son's present age is 7 years

Answer 2

Given : The Father's present age is equal to square of his Son's present age & One year ago his age is Eight times his Son's age .

Need To Find : Present age of Father and Son ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say , that the Present age of Son be a years & Father be a² years i.e, Father's present age is equal to square of his Son's present age

⠀☆ One year ago their ages :

• Father's age will be : ( a² – 1 ) years &
• Son's age will be : ( a – 1 ) years .

$\:\bigstar\:\underline{\pmb {\boldsymbol {\:According \:\:To\:\:the \:Question \:\::\:}}}$

⠀▪︎⠀One year ago his ( Father's ) age is Eight times his Son's age .

$\\:\implies \sf \: Father's \:_{\:(\:Age\:)\:} \:\:=\:8\:\Big\{ Son's \:_{\:(\:Age\:)\:} \: \Big\}\:$

$:\implies \sf \: a^2 - 1 \:\:=\:8\:\Big\{ \: a - 1 \: \Big\}\:$

$:\implies \sf \: a^2 - 1 \:\:= \: 8a - 8 \:$

$:\implies \sf \: a^2 \:\:= \: 8a - 8 + 1 \:$

$:\implies \sf \: a^2 \:\:= \: 8a - 7 \:$

$:\implies \sf \: a^2 \:-\:8a\:+\:7\:= \: 0 \:$

$:\implies \sf \: a^2 \:-\:7a\:-\:a\:+\:7\:= \: 0 \:$

$:\implies \sf \: a\:(\: a - 7\: ) \:-1\:\:(\: a - 7\: )\:= \: 0 \:$

$:\implies \sf \:(\: a - 1\: )\:(\: a - 7\: )\:= \: 0 \:$

$:\implies \pmb{\sf \:a\:= \: 1\:\:or\:\:7 \:}$

• We know , that ' a ≠ 1 ' , because if a = 1 then , One year ago Son's age will be 0 as it is impossible .

$\\:\implies \sf \:a\:= \: 1\:\:or\:\:7 \: \qquad \Bigg\lgroup \: a \:\neq \:1\:\Bigg\rgroup$

$:\implies \pmb{\sf \:a\:= \:7 \:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

$\bigstar \underline {\pmb{\sf{ \:Their \:Present \:Ages\:\::\:}}}$

• Present age of Son is , a = 7 years &
• Present age of Father is , a² = ( 7 )² = 49 years .

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