CAT 2017 Slot 2 — QA Question 4

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).