In every hour, a cyclist covered 1 km more distance than he was to cover with his original speed on $1×1/4$ hour.

So he covered 96 km distance early by 2 hours.

The original speed of cyclist (km/hr) is

** Option:**

**A.**12

**B.**14

**C.**16

**D.**18

**Answer: A . 12**

** Justification:**

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.