A car can cover a ‘2d’ km distance at the speed of

Solution

A car can cover a ‘2d’ km distance at the speed of ‘B’ km/h in 30 hours. 2d/B = 30 d/B = 15 d = 15B    Eq.(i) The total time taken by the boat to cover ‘d’ km distance in upstream and the same distance in downstream is 40 hours. [d/(B-C)] + [d/(B+C)] = 40 Put Eq.(i) in the above equation. [15B/(B-C)] + [15B/(B+C)] = 40 By solving the above equation, 30B ² = 40B ² − 40C ² 40C ² = 40B ² − 30B ² 40C ² = 10B ² B ² = 4C ² So B = 2C    Eq.(ii) The time taken by the boat to cover 1080 km distance in downstream is 8 hours less than the time taken by the boat to cover 600 km distance in upstream. [1080/(B+C)] = [600/(B-C)] - 8 [600/(B-C)] - [1080/(B+C)] = 8 Put the value of ‘B’ from Eq.(ii) in the above equation. [600/(2C-C)] - [1080/(2C+C)] = 8 [600/C] - [1080/3C] = 8 [600/C] - [360/C] = 8 [240/C] = 8 C = 30 km/h Put the value of ‘C’ in Eq.(ii). B = 2x30 B = 60 km/h Put the value of ‘B’ in Eq.(i). d = 15x60 = 900 km Time taken by the boat to cover (d-210) km distance in still water = (d-210)/B = (900-210)/60 = 690/60 = 11.5 hours (i) [{C(B+C)}/5B] + 1.5 Put the values of ‘B’ and ‘C’ in the above equation. [{30(60+30)}/5x60] + 1.5 [{30x90}/300] + 1.5 9 + 1.5 10.5 The above given equation is not correct. Because the required time is not obtained from it. (ii) [{C(B-C)}/B] - 3.5 Put the values of ‘B’ and ‘C’ in the above equation. [{30(60-30)}/60] - 3.5 [{30x30}/60] - 3.5 15 - 3.5 11.5 The above given equation is correct. Because the required time is obtained from it. (iii) [18B/{C(B-C)}] + 10.3 Put the values of ‘B’ and ‘C’ in the above equation. [(18x60)/{30(60-30)}] + 10.3 [1080/{30x30}] + 10.3 [1080/90] + 10.3 1.2 + 10.3 11.5 The above given equation is  correct. Because the required time is not obtained from it.