Two friends are approaching by two cycles of speed 10 km/hr. Initially they are at a distance of 10km.

They start cycling together. A dog also starts running from one of the ends simultaneously at double the speed of cycle. On reaching the other friend the dog runs back to the first friend. Again dog runs to the other friend and continues to shuttle between them till the friends meet each other.

Now the question is what is the total distance covered by the dog  ?!!!! 

Apart from above answer there is a round about method of solving it.

See, in the first round dog covers a distance of 2/3 part of 10km and second friend covers 1/3 rd part.

Meanwhile first friend also will be covering 1/3 distance. So now the distance left for dog to run is only 10/3km in the second round.

In this again dog covers 1/3 of  10/3km and this continues........

Total distance covered by

the  dog = 2/3 . 10 + 2/3 . 10/3 + 2/3 . 1/3 . 10/3  + 2/3 . 1/3 . 1/3 . 10/3 + 2/3 . 1/3 . 1/3 . 1/3 .10/3 + . . . . + . . 

               =  6.66      +   2.22        +   0.74    +      0.246       +   0.082         + . . . . . . .+  . . . . .              

              = 9.948  ie. approaching to 10km 

   @ sachinguptaiit  Ofcourse your answer is eligant and apt

lil master. thts da sumin of da infinity series related to 20 km/h relative velocity. it was a method used by the gr8 mathematician jon von neumann.