John                          Paul

At first            2u  x5 = 10u              3u x 4   = 12u

After              +84 x 5 = 420           -25 x 4 = -100

New                 4p x5 = 20p              5p x 4 = 20p

10u + 420 = 12u -100

2u = 520

Hence John has $520 at first.

Please  click on “Accept Answer” if you are ok with it.  The answer is correct.

Also why did John became = Paul for this question? 

Why do we have to multiply by 5 and 4

Due to the change in ratios before and after, there are 2 unknowns here, u and p.  So when you make one of the ratio the same which is the 4p:5p by multiplying the whole equation by a factor which makes them the same, the p can be eliminated and you focus only to find u.