Ram and Shyam run a race of 2000m. First, Ram shyam a start of 200m and beats him by 30s. Next, Ram gives Shyam a start of 3min and is beaten by 1000m. Find the speed of the boat in still water and the speed of the river flow.

• let shyam run at the speed of x mts / sec ....
  
  now in the first case... ram gives shyam a start of 200m ... then, when ram runs 2000mts ..
  
  shyam runs 1800-30x mts ...
  
  so the ratio of their speed is 2000/(1800-30x)
  
  for the second case .. shyam has a lead of 3 min that is 180x mts ... then, when ram runs a 1000 mts shyam runs 2000 - 18x mts ,so in this case the ratio of their speed is 1000/(2000-180x) ...
  
  equating the 2 ratios and solving for x we have x = 20/3 mts ....that is shyams speed is 20/3 mts ... so time taken to finish the race is
  
  2000/(20/3) sec = 300 sec = 5 min
  
  now we can go on to solve for rams speed ...
  240sec=4min
  
  therefore
  ram :shyam = 4:5
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