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Question:

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

Explanation:

Let ‘d’ miles be the distance for the onward journey from his home to his hostel.

Now time take for onward jouney = d/60.

For the return journey, time taken to cover half distance (i.e. d/2)

⇒ $\frac{\mathrm{d}}{2}÷25$ = $\frac{\mathrm{d}}{50}$

Now for the return journey, (after half the distance is covered) taking the bypass road will increase the distance by 5 miles i.e., the remaining distance of the journey is 'd/2 + 5' miles

Now, 'd/2 + 5' miles is covered at the speed of 50 miles per hour. 

Sp time taken to cover '$\frac{\mathrm{d}}{2}$ + 5' miles is (d/2 + 5)/50 = $\frac{\mathrm{d}}{100}+\frac{1}{10}$
 
Total time for return journey = $\frac{\mathrm{d}}{50}$ + $\frac{\mathrm{d}}{100}+\frac{1}{10}$ = $\frac{3\mathrm{d}+10}{100}$

Now as time taken for return journey is half an hour more than onward journey.

⇒$\frac{\mathrm{d}}{50}+\frac{1}{2}$ = $\frac{3\mathrm{d}+10}{100}$

Hence, d = 30

Total distance covered (for onward and return journey) = d + d/2 + d/2 + 5

= 30 + 30/2 + 30/2 + 5 = 65 miles

Hence, option (c).