Question

Rohan 's morher is 26 years older than him . The product of their age in years 3 years from now will be 360 . Find the Rohan 's present age

Answer 1

In the above Question , the following information is given -

Rohan 's mother is 26 years older than him .

The product of their age in years 3 years from now will be 360 .

To find -

Find the Rohan 's present age .

Solution -

Here ,

Rohan 's mother is 26 years older than him .

So ,

Let the assume that the present age of Rohan is x years .

According to the given condition ,

Age Of Rohan's mother

=> x + 26 years .

Now ,

After 3 years -

Age Of Rohan

=> x + 3 years .

Age Of Rohan's Mother

=> x + 29 years .

Now ,

The product of their age in years 3 years from now will be 360 .

So ,

( x + 3 )( x + 29 ) = 360

=> x² + 32 x + 87 = 360

=> x² + 32x - 273 = 0

=> x² - 7x + 39x - 273 = 0

=> x ( x - 7 ) + 39 ( x - 7 ) = 0

=> ( x + 39 )( x - 7 ) = 0

The only value of x is 7 as it can't be negative .

Thus , Rohan's present age is 7 years .

_____________

Answer 2

$\huge\sf\pink{Answer}$

☞ Rohan's age = 7 years

☞ Mother' age = 33 years

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Rohan's mother is 26 years older than him

✭ The product of their ages after 3 years will be 360

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ Rohan's Present age?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let Rohan Age be x years

Then Mother Age = (x+26) years

After 3 years,

Rohan Age = n(x+3) years

Mother Age = n(x+26+3) years

Product = 360 years

So now,

➢ $\sf (x+3)(x+26+3)=360$

➢ $\sf (x+3)(x+29)=360$

➢ $\sf x^2+29x+3x+87=360$

➢ $\sf x^2+32x+87=360$

➢ $\sf x^2+32x+87-360=0$

➢ $\sf\green{x^2+32x-273=0}$

By Splitting the Middle term,

➝ $\sf x^2+(39-7)x-273=0$

➝ $\sf x^2+39x-7x-273=0$

➝ $\sf (x+39)-7(x+39)=0$

➝ $\sf\color{red}{(x-7)(x+39)=0}$

Equating with zero,

➳ x-7 = 0

➳ x = 0+7

➳ x = 7

➳ x+39 = 0

➳ x =0-39

➳ x = -39

Hence Age Can't be in negative

$\sf\orange{x=7 years}$

$\sf\dashrightarrow\color{lime}{Rohan \ Age = x = 7 \ years}$

$\sf\dashrightarrow\color{aqua}{Mother \ Age=x+26=7+26=33 \ years}$

$\rule{170}3$