A person cycling at a speed of 30 kmph reaches college from hostel 5 minutes late. If he cycled at a speed of 36 kmph, he would have reached 4 minutes early. Find the distance between the hostel and college?

Question

Question

This question was previously asked in

RPF SI (2018) Official Paper (Held On: 24 Dec, 2018 Shift 1)

Answer 1

Given:

Speed when late = 30 kmph

Time late = 5 minutes = 5/60 hours

Speed when early = 36 kmph

Time early = 4 minutes = 4/60 hours

Formula Used:

Distance = Speed × Time

Calculation:

Let the actual time taken to reach college be t hours.

Time taken when late = t + 5/60 hours

Time taken when early = t - 4/60 hours

Distance when late = Distance when early

30 × (t + 1/12) = 36 × (t - 1/15)

⇒ 30t + 2.5 = 36t - 2.4

⇒ 30t - 36t = -2.4 - 2.5

⇒ -6t = -4.9

⇒ t = 4.9/6

⇒ t = 0.8167 hours

Distance = 30 × (0.8167 + 1/12)

Distance = 30 × 0.9

Distance = 27 km

The distance between the hostel and college is 27 km.