Question

A mothers age after 5 years will be twice the age of her daughter. The difference of their ages is 19. What is the age of mother?​

Answer 1

Solution:-

Let

Daughter age = x

Mother age = y

So

Difference of their age is 19

y - x = 19 .......(i)eq

So age after 5 years

:- Daughter age x + 5

:- Mother age = y + 5

We can write

Given :-

( y + 5 ) = 2( x + 5)

By solving

y + 5 = 2x + 10

2x - y = -5 .....(ii)eq

Using elimination method

Add i and ii eq

y - x + 2x - y = 19 - 5

x = 14

Now put the value of x on ( i) eq

y - x = 19

y - 14 = 19

y = 19 + 14

y = 33

So

Mother age is 33

Answer 2

Solution :

Le the Mother's age be R years & daughter age be M years respectively;

$\longrightarrow\sf{R-M=19}\\\\\longrightarrow\sf{R=19+M.......................(1)}$

&

$\underbrace{\bf{After\:5\:years\::}}}$

The age of Mother will be (R+5) years .

The age of Daughter will be (M+5) years .

Now;

$\longrightarrow\sf{(R+5) = 2(M+5)}\\\\\longrightarrow\sf{R+5=2M+10}\\\\\longrightarrow\sf{R-2M=10-5}\\\\\longrightarrow\sf{R-2M=5}\\\\\longrightarrow\sf{19+M-2M=5\:\:[from(1)]}\\\\\longrightarrow\sf{19-M=5}\\\\\longrightarrow\sf{-M=5-19}\\\\\longrightarrow\sf{\cancel{-}M=\cancel{-}14}\\\\\longrightarrow\bf{M=14\:years}$

∴ Putting the value of M in equation (1),we get;

$\longrightarrow\sf{R=19+14}\\\\\longrightarrow\bf{R=33\:years}$

Thus;

The age of Mother's will be 33 years .