Question

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Five year hence the age of job will be three times that of his son .Five year ago Jacobs age was seven times that of his son what are their present age




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Answer 1

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$

Five year hence the age of job will be three times that of his son .Five year ago Jacobs age was seven times that of his son what are their present age

$\huge\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

Let the present age of Jacob be = x

The present age of his son be = y

After 5 year ;

The age of Jacob = ( x + 5 ) years

The age of son = ( y + 5 ) years

According to the problem ;

$~~~~~~~~~~~~~\longrightarrow$ $\bold{x + 5 = 3(y + 5)}$

$~~~~~~~~~~~~~\longrightarrow$ $\bold{x + 5 = 3y + 15}$

$~~~~~~~~~~~~\longrightarrow$ $\bold{x - 3y = 15 - 5}$

$~~~~~~~~~~~~\longrightarrow$ $\bold{x - 3y = 10}$ ---------(1)

Before 5 years ;

Age of Jacob = ( x - 5 ) years

Age of his son = ( y - 5 ) years

According to the problem ;

Age of Jacob = 7 ( age of his son )

$~~~~~~~~~~\longrightarrow$ $\bold{x - 5 = 7(y - 5)}$

$~~~~~~~~~~\longrightarrow$ $\bold{x - 5 = 7y - 35}$

$~~~~~~~~~~\longrightarrow$ $\bold{x - 7y = - 35 + 5}$

$~~~~~~~~~~\longrightarrow$ $\bold{x - 5 = - 30}$ -----------(2)

$~~~~~~~~~~~~~From \:eq(1) \:We \:have$

$~~~~~~~~~~\longrightarrow$ $\bold{x - 3y = 10}$

$~~~~~~~~~~\longrightarrow$ $\bold{x = 10 + 3y}$ ---------(3)

$~~~~~~~~~~~~~~~~Substitute \:eq(3) \:in (2)$

$~~~~~~~~~~\longrightarrow$ $\bold{10 + 3y - 7y = - 30}$

$~~~~~~~~~~\longrightarrow$ $\bold{10 - 4y = - 30}$

$~~~~~~~~~~\longrightarrow$ $\bold{ - 4y = - 30 - 40}$

$~~~~~~~~~~\longrightarrow$ $\bold{ -4y = - 40}$

$~~~~~~~~~~\longrightarrow$ $\bold{ y = \frac{-40}{-4}}$

$~~~~~~~~~~\longrightarrow$ $\bold{ y =\cancel\frac{-40}{-4}}$

$~~~~~~~~~~\longrightarrow$ $\bold{ y = 10}$

Present age of the son is 10 year's

Now ;

$~~~~~~~~~~~~~~~~Substitute \:y = 10 \:in \:eq(3)$

$~~~~~~~~~~~~~\longrightarrow$ $\bold{x = 10 + 3y}$

$~~~~~~~~~~~~~\longrightarrow$ $\bold{x = 10 + 3(10)}$

$~~~~~~~~~~~~\longrightarrow$ $\bold{x = 40}$

The age of Jacob is 40 years.

Answer 2

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