There are 5 racing tracks and 25 horses At a time you can conduct race for 5 horses in the five available tracks What will be the minimum number of trials needed to find out the ultimate winner run?

Let's take an assumption, each horse runs at uniform speed every time. They all have different but fixed speed tag.

Step 1) Divide the 25 horses into 5 groups. Each group will have 5 horses each.

Step 2) Conduct 5 races for the 5 groups.

Step 3) Conduct an another race with each group winners. (i.e. Fastest from Group 1, Fastest from Group 2, ... , and Fastest from Group 5)

Step 4) Choose the winner from the Step 3. That will be fastest horse. (So, it needs only 6 races to find out the fastest horse of all the 25 horses)

Additionally,

Step 5) Name the horses as below:

{a1,a2,..., a5}--> For the group which has the fastest horse after Step 3 (6th Race)

{b1,b2,...,b5}---> For the group which has the 2nd fastest horse after Step 3

{c1,c2,...,c5}----> For the group which has the 3rd fastest horse after Step 3

{d1,d2,...,d5}---> For the group which has the 4th fastest horse after Step 3

{e1,e2,...,e5}---> For the group which has the 5th fastest horse after Step 3

Where according to their speed, a1>a2>..>a5; b1>b2>..>b5; c1>c2>..>c5; d1>d2>..>d5 and e1>e2>..>e5, also, a1>b1>c1>d1>e1, but not necessarily, b1>a2, c1>b2 etc. [Clearly a1 is the fastest horse]

Step 6) Conduct a race with a2, a3, b1, b2 and c1 to find out the 2nd fastest and 3rd fastest of all the 25 horses.

So, we need to conduct only 7 races to find out the top 3 fastest horses!