Question

5years ago a man was 7 time as old as his son. after 5years he will be thrice as old as his son. find their present age​

Answer 1

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

$\sf{The \ ages \ of \ the \ man's \ and \ his \ son}$

$\sf{are \ 40 \ and \ 10 \ years \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{5 \ years \ ago \ a \ man \ was \ 7}}$

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

$\sf{\implies{After \ 5 \ years \ he \ will \ be \ thrice}}$

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

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

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

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

$\sf{Let \ the \ age \ of \ the \ man \ be \ x \ years}$

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

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

$\sf{x-5=7(y-5)}$

$\sf{x-5=7y-35}$

$\sf{\therefore{x-7y=-30...(1)}}$

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

$\sf{x+5=3(y+5)}$

$\sf{x+5=3y+15}$

$\sf{\therefore{x-3y=10...(2)}}$

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

$\sf{x-3y=10}$

$\sf{-}$

$\sf{x-7y=-30}$

___________________

$\sf{4y=40}$

$\sf{y=\frac{40}{4}}$

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

$\sf{Substitute \ y=10 \ in \ equation(2)}$

$\sf{x-3(10)=10}$

$\sf{x-30=10}$

$\sf{x=10+30}$

$\boxed{\sf{\therefore{x=40}}}$

$\sf{Man's \ age=40 \ years.}$

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

$\sf\purple{\tt{\therefore{The \ ages \ of \ the \ man's \ and \ his \ son}}}$

$\sf\purple{\tt{are \ 40 \ and \ 10 \ years \ respectively.}}$

Answer 2

GIVEN...

• 5 years ago, man was 7 times as old as his son.
• five years hence he will be three times as old as his son.

TO FIND...

• present age of man and his son.

SOLUTION...

$\red{let \: 5 \: years \: ago \: the \: age \: of \: son \: be \: X \: years \: .So \: age \: of \: father \: be \: 7x \: years .\: }</p><p> \\ \\ </p><p> \therefore \: present \: age \: of \: son = (x + 5)years \\ \: \: \: and \: present \: age \: of \: father = (7x + 5)years \\ \\ after \: 5 \: years ... \\age \: of \: son \: = x + 5 + 5 =( x + 10)years \\ age \: of \: father \: = 7x + 5 + 5 = (7x + 10)years \\ \\ \red{A.T.Q.} \\ \\ = > 7x + 10 = 3(x + 10) \\ = > 7x + 10 = 3x + 30 \\ = > 7x - 3x = 30 - 10 \\ = > 4x = 20 \\ = > x = \frac{20}{4} \\ \\ = > x = 5 \\ \\ </p><p>$

FINAL ANSWER...

• Therefore, the present age of sun= x+5=10 years.
• And the present age of father=7x+5=40 years.