Let the speed of Ram and Shyam be x m/s and y m/s respectively.

Since their speeds are in the ratio 5 : 4, we have x/y = 5/4

Now, for the given race, the total distance to be covered is 4 km = 4000 m.

Time taken by Ram to cover 4000 m = 4000/x = 4000/5x

Time taken by Shyam to cover 4000 m = 4000/y = 4000/4y

Since the time taken by Ram is less than that of Shyam, Ram will complete the race before Shyam.

Therefore, the number of times the winner (Ram) passes the other (Shyam) can be calculated as follows:

Number of times the winner (Ram) passes the other (Shyam) = (Distance covered by the winner)/(Distance covered by the other)

Distance covered by Ram in 4000/5x = 4000/4y

Distance covered by Ram in 4000/4x = 4000/5y

Therefore, the number of times the winner (Ram) passes the other (Shyam) = 4000/4x / 4000/5y

Number of times the winner (Ram) passes the other (Shyam) = 4x/5y = 5/4

Since the ratio of the speed of Ram and Shyam is 5 : 4, the number of times the winner (Ram) passes the other (Shyam) is 3.

Hence, the correct answer is Option B. Ram passes Shyam thrice.

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