Math, asked by Anonymous, 9 months ago

style="color:cyan;font-family:cursive;background:black;font size:25px;"> Q. A man is 4 times as old as his son . After 16 years he will. be only twice as old as his son . Find their present ages... [/tex]. $<body aquacolor=b>$ <br /> $\large\orange{}$ <br /> $<font color=red>$ <br /> $<marquee>GOOD MORNING\ \textless \ br /\ \textgreater \ PLEASE SOLVE </marquee>$

Answers

Answered by Saby123

3

Correct Question -

A man is 4 times as old as his son .

After 16 years he will. be only twice as old as his son .

Find their present ages.

Solution -

Let the age of the son be x years .

So, the age of the man is 4x years .

After 16 years,

Age Of Son = x + 16 years .

Age of Man = 4x + 16 years.

Now , we have the following information given -

After 16 years he will. be only twice as old as his son .

Btw ,

4x + 16 = 2(x + 16 )

=> 4x + 16 = 2x + 32

=> 2x = 16

=> x = 8

So,

Age of Man = 4x = 32 .

Therefore Present Age of Son = x = 8 years.

Present Age of Man = 4x = 32 years.

Answered by Anonymous

9

$\blue{Question}$

A man is 4 times as old as his son. After 16 years he will be only twice as old as his son.

Find their present ages.

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ present \ age \ of \ man \ and \ his }$

$\sf{son \ is \ 32 \ and \ 8 \ years \ respectively.}$

$\orange{Given:}$

$\sf{\implies{A \ man's \ age \ is \ 4 \ times \ his \ son's \ age}}$

$\sf{\implies{After \ 16 \ years \ he \ will \ be \ twice}}$

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

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

$\sf{Their \ present \ ages.}$

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

$\sf{Let \ the \ present \ age \ of \ the \ man \ be}$

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

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

$\sf{\implies{x=4y}}$

$\sf{\implies{x-4y=0...(1)}}$

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

$\sf{\implies{x+16=2(y+16)}}$

$\sf{\implies{x+16=2y+32}}$

$\sf{\implies{x-2y=32-16}}$

$\sf{\implies{x-2y=16...(2)}}$

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

$\sf{x-2y=16}$

$\sf{-}$

$\sf{x-4y=0}$

___________________

$\sf{\implies{2y=16}}$

$\sf{\implies{y=\frac{16}{2}}}$

$\sf{\implies{y=8}}$

$\sf{Substitute \ y=8 \ in \ equation (1),\ we \ get}$

$\sf{\implies{x-4(8)=0}}$

$\sf{\implies{x-32=0}}$

$\sf{\implies{x=32}}$

$\sf\purple{\tt{\therefore{The \ present \ age \ of \ man \ and \ his }}}$

$\sf\purple{\tt{son \ is \ 32 \ and \ 8 \ years \ respectively.}}$

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