Question

After 2 years of time, Paul will be 3 times as old as Alice. Presently he is 6 times as old. How old is Paul now?

Answer 1

        Paul = 6 * Alice      ---- 1

    Paul +2 = 3 (Alice + 2 )
    Paul + 2 = 3 Alice + 6 
     Paul = 3 Alice + 4        ----- 2
 
    equate equation 1 and 2:
              6 * Alice = 3 * Alice  + 4 
                  3 * Alice = 4            

                       Alice = 4/3 years = 16 months

           Paul = 6 * 4/3 years = 8 years

Answer 2

Let the present age of Paul be x and 
Let the present age of Alice be y.
Then A.T.Q
1.  x = 6y  --------------------------------(1)

2.  x +2 = 3×(y + 2)
 x + 2 = 3y + 6  --------------------------(2)

Putting the value of x in (2)
 
   6y - 3y = 4
   3y= 4
    y = 4/3    

   For x = 6y
         x = 6 × 4/3
         x= 8.

  Hence the age of Paul is 8 years.