The best approach in my view is like this:

Check from the answer options.

As one horse completes the lap in 9 minutes and the other in 12 minutes,

the answer is definitely greater than 12, because by 12 minutes, faster on completes 12/9 = 1.33 laps and the slower one completes only 1 lap, which results in a gap of 1.33 - 1 = 0.33 laps, which is less than 1 lap.

The only option looks feasible is option-A, ie., 36 min.

With out checking we can go for that. But let us check:

After 36 min, faster one completes 36/9 = 4 laps and

slower one completes 36/12 = 3 laps.

The faster one covered exactly one more lap than the slower one did.

Answer

'A'
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Ravi Sankar Vemuri