A train covered a certain distance at a uniform speed.  If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time.   And if the train were slower by 6km/hr, it would have taken 6 hours more than the scheduled time. Find the distance of the journey.

Ans:    Let the speed of the train by x km/hr

And the time taken by it by y

Now distance traveled by it is x x y = xy

APQ:

I--- (x + 6) (y - 4) = xy

4x - 6y = -24

=> 2x - 3y = -12 ----------------(1) II--- (x - 6) (y+ 6) = xy

6x - 6y= 36

=> x- y= 6      ----------------(2) Solving for x and y we get y = 24,  x = 30

So the distance       =30 × 24

= 720 km