In a 100 m race,Neeraj can beat Siddharth by 20 m and Siddharth can beat Rohit by 20 m . By what distance will Neeraj beat Rohit in a 500 m race?

180m Per q If Neeraj runs 100m Siddharth ran 80m and when Siddharth ran 100m Rohit ran 80m in the same time. Note their speeds are constant throughout and will be in the ratio N/S=5/4 and S/R=5/4, Making S common in both we get ratio of speeds of N:S:R as 25:20:16. In a 500m race N will run (25*20=500) and so R will run (16*20=320). Hence, in a 500m race N beats R by 180m.

In the last line of solution how is the time 20 unit is calculated?

I think you are asking why we are multiplying 20. So the required ratios of speed we get for N:S:R are 25:20:16. Which means since they all run for the same time the distance and speed ration will be same. If N run 25 kms, S will run 20 kms and R will run 16 kms. In the question they ask by how much will N beat R by meaning N would have run the entire 500m. Hence 25*(20) gives us 500. Since we are multiplying 20 for N we will also multiply 20 for R and then R would have run (16*20-320 m ) and thats how N beats R by 180m in a 500 m race. We are simply multiplying 20 because 25*20 gives us 500. 20 units as u mentioned earlier isnt time or anything.

Thank you