A person cycles from hostel to college at a speed of 20 kmph and reaches 13.5 minutes late. If he cycles at a speed of 24 kmph and reaches early by 13.5 minutes, find the distance between hostel and college. (In km)

Correct option is B

Speed1 = 20 km/hr (late by 13.5 minutes)
Speed2 = 24 km/hr (early by 13.5 minutes)

Total time difference = 27 minutes
= 27 / 60 hours
= 0.45 hours

Let distance = d km

d/20 − d/24 = 0.45

LCM = 120

(6d − 5d) / 120 = 0.45

d / 120 = 0.45

d = 54 km