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A train covered a certain distance at a uniform speed. If the train would have been 10km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Let the speed of the train = x km/hr  
Let the time taken for the entire journey = y hrs
We know that  speed = distance / time
So , distance  = xy
Therefore in the first case xy = (x +10)(y - 20)
i.e 2 x – 10 y + 20 =0………(1)
and ,In the first case , xy =  (x -1) ( y +3)
i.e  3x – 10 y – 30 =  0…………(2)
Now, from (1) and (2) , we get
 x = 50 and y = 12 
Therefore the speed of the train = 50 km/hr
Let the time taken for the entire journey = 12 hrs
distance  =  50 x 12 = 600 km.


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