Suppose the original speed is x km/hr.
Distance covered in $ 1 1/4(=5/4)hr =5/4 × km $
New speed =  $ (5/4x + 1) {km} / {hr} $
By hypothesis,
$ 96/(5/4x+1) = 96/x-2  $
or $ 384x = 480x - 10x^2 + 384 - 8x $
or $ 10x^2 - 88x - 384 = 0 $
or $ 5x^2 - 44x - 192 = 0 $
or $ 5x^2 - 60x + 16x - 192 = 0 $
or (5x + 16) (x - 12) = 0
$ x =  - 16/5 , x = 12 $
Since speed can`t be - ve,
x = 12 km/hr.