Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is

Let the distance between the home and office be $$2x$$ miles
Time taken for going in the morning = $$\frac{2x}{60}$$ hrs
Time taken for going back in the evening = $$\frac{x}{25} + \frac{x+5}{50}$$. hrs
It is given that he took 30 minutes (0.5 hrs) more in the evening

Hence $$\frac{2x}{60}$$ hrs + 0.5 = $$\frac{x}{25} + \frac{x+5}{50}$$
Solving for x, we get x = 15 miles.
Total distance traveled = 2x + x + x + 5 = 4x + 5 = 65 Miles