Question

mother tells her son 5years ago I was 5times as old as you were. After 10 years I will be two times as old as you will be.​

Answer 1

let mother age be x

so before 5 yrs =x-5

5 times means=5x-5

after 10 yrs =15x-5

two times =2(15x-5)

30x-5=0

x=35yrs

his mother present age =35yrs

hope it helped u

Answer 2

Let,

current age of mother = x yrs

and current age of her son = y  yrs

then,

5 years ago

age of mother = (x - 5) yrs

age of son = ( y - 5) yrs

A.T.Q.

x - 5 = 5 ( y - 5)

x - 5 = 5 y - 25

x - 5 y - 5 + 25 = 0

x - 5 y + 20 = 0  

x = 5 y - 20    ----equation (1)

NOW,

10 years hence

age of mother = (x + 10)  yrs

age of son = ( y+10)  yrs

A.T.Q

x + 10 = 2 ( y + 10)

x + 10 = 2 y + 20

x - 2 y + 10 - 20 = 0

x - 2 y - 10 = 0

( substituting equation (1) here )

( 5 y - 20 ) - 2 y - 10 = 0

5 y - 20 - 2 y - 10 = 0

3 y - 30 = 0

3 y = 30

y = 30 /3

y = 10

(putting y = 10 in equation (1))

x = 5 y - 20

x = 5 ( 10 ) - 20

x = 50 - 20

x = 30

$\red{\boxed{\underline{Hence\:current\: age\:of\:mother\:is\:30\:years}}}$

AND

$\pink{\boxed{\underline{current\:age\:of\:son\:will\:be\:10\:years}}}$