Total time taken by a person in going to a place by walking and returning on cycle is 5 hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to walk both ways is

Let the time taken to walk one way be W and the time taken to cycle one way be C. According to the first condition, walking one way and cycling back takes 5 hours 45 minutes. So, W plus C equals 5 hours 45 minutes. The second condition states that cycling both ways saves 2 hours. This means 2C is equal to 5 hours 45 minutes minus 2 hours, which is 3 hours 45 minutes. To find the time taken to walk both ways, which is 2W, we can use the logic that 2W plus 2C equals twice the time of a single round trip. Twice of 5 hours 45 minutes is 11 hours 30 minutes. Since 2W plus 2C equals 11 hours 30 minutes, and we know 2C is 3 hours 45 minutes, we subtract 3 hours 45 minutes from 11 hours 30 minutes. 11 hours 30 minutes minus 3 hours 45 minutes equals 7 hours 45 minutes. Therefore, the time taken to walk both ways is 7 hours 45 minutes. The correct option is B.