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)

This question was previously asked in
UP Police SI (दरोगा) Official PYP (Held On: 12 Nov 2021 Shift 3)
View all UP Police Sub Inspector Papers >
  1. 52
  2. 54
  3. 48
  4. 50

Answer (Detailed Solution Below)

Option 2 : 54
Free
यूपी पुलिस SI (दरोगा) सामान्य हिंदी मॉक टेस्ट
44.9 K Users
20 Questions 50 Marks 10 Mins

Detailed Solution

Download Solution PDF

Given:

Speed at which the person is late = 20 kmph

Time late = 13.5 minutes = 13.5/60 = 0.225 hours

Speed at which the person is early = 24 kmph

Time early = 13.5 minutes = 13.5/60 = 0.225 hours

Formula Used:

Distance (D) = Speed × Time

Time difference = Difference in distances / Relative speed

Calculation:

Let the distance between the hostel and college = D km.

Time taken at 20 kmph = D / 20

Time taken at 24 kmph = D / 24

Time difference = (D / 20) - (D / 24)

It is given that the total time difference is the sum of 13.5 minutes late and 13.5 minutes early, which is 27 minutes = 27 / 60 = 0.45 hours.

⇒ (D / 20) - (D / 24) = 0.45

Taking LCM of 20 and 24:

⇒ (6D - 5D) / 120 = 0.45

⇒ D / 120 = 0.45

⇒ D = 0.45 × 120

⇒ D = 54 km

The distance between the hostel and college is 54 km.

Latest UP Police Sub Inspector Updates

Last updated on Jun 5, 2025

-> The UP Police Sub Inspector 2025 Notification will be released by 15th June for 4543 vacancies.

-> A total of 35 Lakh applications are expected this year for the UP Police vacancies..

-> The recruitment is also ongoing for 268  vacancies of Sub Inspector (Confidential) under the 2023-24 cycle.

-> The pay Scale for the post ranges from Pay Band 9300 - 34800.

-> Graduates between 21 to 28 years of age are eligible for this post. The selection process includes a written exam, document verification & Physical Standards Test, and computer typing test & stenography test.

-> Assam Police Constable Admit Card 2025 has been released.

More Speed Time and Distance Questions

Get Free Access Now
Hot Links: teen patti customer care number teen patti gold new version teen patti master list