The time taken by the boat to cover (d+130) km distance in downstream is 1.9 hours less than the time taken by the same boat to cover (d-45) km distance in upstream. The same boat can cover (d+20) km distance in still water in 11.75 hours. If the speed of the stream is 75% less than the speed of the boat, then find out the value of ‘d’.

Solution

Let’s assume the speed of the boat in still water and the speed of the stream are ‘B’ and ‘C’ respectively. If the speed of the stream is 75% less than the speed of the boat. C = (100-75)% of B C = 25% of B C = (25/100) x B C = (1/4) x B B = 4C    Eq. (i) The same boat can cover (d+20) km distance in still water in 11.75 hours. (d+20)/B = 11.75 Put the value of ‘B’ from Eq. (i) in the above equation. (d+20)/4C = 11.75 (d+20)/47 = C    Eq. (ii) The time taken by the boat to cover (d+130) km distance in downstream is 1.9 hours less than the time taken by the same boat to cover (d-45) km distance in upstream. [(d+130)/(B+C)] = [(d-45)/(B-C)] - 1.9 Put the value of ‘B’ from Eq. (i) in the above equation. [(d+130)/(4C+C)] = [(d-45)/(4C-C)] - 1.9 [(d+130)/5C] = [(d-45)/3C] - 1.9 Put the value of ‘C’ from Eq. (ii) in the above equation. [47(d+130)]/[5(d+20)] = [47(d-45)]/[3(d+20)] - 1.9 By solving the above equation, the value of ‘d’ = 450