Question

Two years ago , a man was 5 times as old as his son. Two years later his age will be 8 more than three times theage of the son.
Find the present ages of the man and his son.

Pl could you answer me fast

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ man's \ age \ and \ his \ son's \ age \ is}$

$\sf{42 \ years \ and \ 10 \ years \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Two \ years \ ago, \ a \ man \ was \ 5}}$

$\sf{times \ as \ old \ as \ his \ son.}$

$\sf{\implies{Two \ years \ later \ his \ age \ will \ be}}$

$\sf{8 \ more \ than \ three \ times \ the \ age \ of}$

$\sf{the \ son.}$

$\sf\pink{To \ find:}$

$\sf{Present \ ages \ of \ the \ man \ and \ his \ so.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ man's \ age \ be \ x \ years \ and}$

$\sf{his \ son's \ age \ be \ y \ years.}$

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

$\sf{x-2=5(y-2)}$

$\sf{\therefore{x-5y=-8...(1)}}$

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

$\sf{x+2=3(y+2)+8}$

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

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

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

$\sf{-}$

$\sf{x-5y=-8}$

____________________

$\sf{\therefore{2y=20}}$

$\sf{\therefore{y=\frac{20}{2}}}$

$\boxed{\sf{\therefore{y=10}}}$

$\sf{Substitute \ y=10 \ in \ equation (1)}$

$\sf{x-5(10)=-8}$

$\sf{\therefore{x-50=-8}}$

$\sf{\therefore{x=-8+50}}$

$\boxed{\sf{\therefore{x=42}}}$

$\sf{\therefore{Man's \ age=42 \ years}}$

$\sf{His \ son's \ age=10 \ years}$

$\sf\purple{\tt{\therefore{The \ man's \ age \ and \ his \ son's \ age \ is}}}$

$\sf\purple{\tt{42 \ years \ and \ 10 \ years \ respectively.}}$

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{Two \ years \ ago , \ a \ man \ was \ 5 \ times \ as \ old}[tex]</p><p>[tex]\rm{as \ his \ son. \ Two \ years \ later \ his \ age}$

$\rm{will \ be \ 8 \ more \ than \ three \ times \ the \ age }$

$\rm{the \ son. \ Find \ the \ present \ ages \ of \ the}$

$\rm{man \ and \ his \ son.}$

_________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\tt{\pink{\star{\blue{The \ present \ age \ of \ man \ : \ 42 \ yrs.}}}}$

$\tt{\pink{\star{\blue{The \ present \ age \ of \ son \ : \ 10 \ yrs.}}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{\longrightarrow{Two \ years \ ago , \ a \ man \ was \ 5 \ times \ as }}$

$\rm{old \ as \ his \ son. }$

$\rm{\longrightarrow{Two \ years \ later \ his \ age \ will \ be \ more } }$

$\rm{\longrightarrow{than \ three \ times \ the \ age \ of \ the \ son}}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Present \ age \ of \ the \ man \ and \ his \ son}$

_________________________________________

$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{We \ are \ given \ that ,}$

$\rm{\longrightarrow{Two \ years \ ago , \ a \ man \ was \ 5 \ times \ as }}$

$\rm{old \ as \ his \ son. }$

$\rm{\longrightarrow{Two \ years \ later \ his \ age \ will \ be \ more } }$

$\rm{\longrightarrow{than \ three \ times \ the \ age \ of \ the \ son}}$

$\rm{Let, \ the \ present \ age \ of \ the \ man \ be \ m}$

$\rm{and \ the \ present \ age \ of \ son \ be \ n}$

$\rm\therefore{According \ to \ first \ condition}$

$\rm\implies{( \ m-2 \ ) \ = \ 5( \ n-2 \ ) }$

$\rm\implies{( \ m-2 \ ) \ = \ 5n-10 }$

$\rm{\therefore{m-5n \ = \ -8.......(a)}}$

$\rm{Now,}$

$\rm\therefore{According \ to \ second \ condition}$

$\rm\implies{( \ m+2 \ ) \ = \ 8 \ + \ 3( \ n+2 \ ) }$

$\rm\implies{( \ m+2 \ ) \ = 3n \ + \ 14 }$

$\sf{\therefore{m-3n \ = \ 12........(b)}}$

$\sf{Subtract \ equation \ (a) \ from \ equation \ (b)}$

$\rm{We \ get }$

$\rm{\therefore{2n=20}}$

$\rm{\therefore{n=\frac{20}{2}}}$

$\rm{\therefore{\red{\boxed{\green{y=10}}}}}$

$\rm{Putting \ n=10 \ in \ equation (b)}$

$\rm{m-5(10)=-8}$

$\rm{\implies{m-50=-8}}$

$\rm{\implies{m=-8+50}}$

$\rm{\therefore{\red{\boxed{\green{m=42}}}}}$

$\rm{\longrightarrow{Man's \ age=42 \ years}}$

$\rm{\longrightarrow{His \ son's \ age=10 \ years}}$

$\tt{\pink{\star{\blue{The \ present \ age \ of \ man \ : \ 42 \ yrs.}}}}$

$\tt{\pink{\star{\blue{The \ present \ age \ of \ son \ : \ 10 \ yrs.}}}}$

________________________________________

$\tt\orange{Hope \ it \ Helps \ :))}$