Question

Four years ago Jane was twice as old as Sam. Four years on from now Sam will be 3/4 of Jane age?what is Jane present age

Answer 1

Let Jane's current age as J and Sam's current age as S 

4 years ago 
J-4 =2(S-4) 
==> J-4 = 2S -8 ------Eqn 1 

After 4 years 

3/4(J+4) = S+4 

==> 3(J+4) = 4(S+4) 

==> 3J+12 = 4S+16 ----Eqn 2 

Eqn 1 * 3 ==> 3J-12 = 6S-24 
Eqn 2 ==> 3J+12 = 4S+16 
------------------------------------- 
Eq1 -Eq2 ==> -24 =2S-40 
==> 16 = 2S 
==> S = 8 

Sams's current age S = 8 

To find J 
Eqn 1 ==> J-4 = 2S-8 
==> J = 2S -4 
==> J =2*8 - 4 
==> j = 12 
Jane's current Age J = 12

Answer 2

Let the present age of Jane be x years.

Let the present age of Sam be y years.



Given that 4 years ago, Jabe was twice as old as sam.

x - 4 = 2(y - 4)

x - 4 = 2y - 8

x = 2y - 4  -------------- (1)



Given that 4 years from now, sam will be 3/4 of Jane age.

(3/4) * (x + 4) = y + 4

3(x + 4) = 4(y + 4)

3x + 12 = 4y + 16

3x = 4y +  4   --------------- (2)


Substitute (1) in (2), we get

3(2y - 4) = 4y + 4

6y - 12 = 4y + 4

2y = 16

y = 8


Substitute y = 8 in (1), we get

x = 2(8) - 4

   = 16 - 4

   = 12.


Therefore the present age of Jane = 12 years.

                  The present age of Sam = 8 years.



Hope this helps!