Question

the sum of the ages of seema and gaurav is 31 years.after 10 years the ratio of their ages will be 8:9. find their present ages

Answer 1

$\Huge\textbf{Solution}$

$\textbf{Let the Present age of Seema be x}$

$\textbf{so the present age of Gaurav = (31 - x)}$

$\textbf{After 10 years :}$

$\textbf{Age of Seema =(x + 10) years}$

$\textbf{Age of Gaurav = (31 - x ) + 10 years}$

$\textbf{=(31 - x + 10 )years}$

$\textbf{=(41 - x )years}$

$\textbf{According to the Question we have}$

$\bf \dfrac{x + 10}{41 - x} = \dfrac{8}{9}$

$\mathbf{9(x + 10) = 8(41 - x) }$

$\mathbf{ 9x + 90 = 328 - 8x }$

$\mathbf{ 9x + 8x = 328 - 90}$

$\mathbf{ 17x = 238 }$

$\bf{ x = \dfrac{238}{17} }$

$\mathbf{ x = 14}$

$\textbf{So the present age of Seema}$

$\textbf{= x years}$

$\mathbf{ = 14 years}$

$\textbf{Present age of Gaurav = (31-x ) years}$

$\textbf{= (31 - 14)}$

$\mathbf{= 17 years}$

$\huge\textbf{Thanks}$

Have a colossal day ahead

$\Huge\mathfrak{Be}$ $\Huge\mathfrak{BrainlY}$

Answer 2

Hey !!





Let present age of Seema and gaurav be X and Y years respectively.




A/C


X + Y = 31 -----------(1)


After 10 years age of Seema = ( X + 10) years.


After 10 years age of gaurav = ( Y + 10 ) years.



A/C



X + 10 / Y + 10 = 8/9


9 ( X + 10 ) = 8 ( y + 10 )



9X + 90 = 8Y + 80



9X - 8Y = 80 - 90


9X - 8Y = -10 --------(2)


From equation (1) , we get




X + Y = 31


X = ( 31 - Y ) -----------(3)


Putting the value of X in equation (2) , we get


9X - 8Y = -10



9 ( 31 - Y ) - 8Y = -10



279 - 9Y - 8Y = -10




-17Y = -10 - 279



-17Y = -289


Y =17


Putting the value of Y in equation (3) , we get


X = ( 31-Y ) = 31 - 17 = 14


Hence,

Present age of Seema = X = 14 years.

And,

Present age of gaurav = Y = 17 years.