At his usual speed a cyclist covers a certain distance in 8 hours. When the speed of cycle is increased by 4 km/hr the same distance can be covered in 6 hours. Find the distance.

96 km

Let the usual speed of the cyclist be $x\text{ km/h}$.

Then the increased speed is $x + 4\text{ km/h}$.

Since the distance is the same:

$8x = 6(x + 4)$

$8x = 6x + 24$

$2x = 24$

$x = 12\text{ km/h}$

Now, the distance is:

$\text{Distance} = \text{Speed} \times \text{Time} = 12 \times 8 = 96\text{ km}$