Question

Arvind went from point A to B and Surubhi from B to A. They met somewhere between continuing their journey. Arvind took 6 hours and Surubhi took 24 hours to reach the respective destinations after meeting. If Aravind traveled 54 Kmph, what is the distance AB.

Answer 1

Let \(a\) be the speed of Arvind and \(s\) be the speed of Surbhi. Let them meet after \(t\) hours. Arvind traveled \(s \times t\) distance in 6 hours and Surbhi traveled \(a \times t\) distance in 24 hours. \(⇒ s \times t = a \times 6\) and \(a \times t = s \times 24\). \(⇒ t^2 = 6 \times 24\). \(⇒ t^2 = 144\). \(⇒ t = \sqrt{144}\). \(⇒ t = 12\). Given that, \(a = 54\). \(⇒ s \times 12 = 54 \times 6\). \(⇒ s = \frac{54 \times 6}{12}\). \(⇒ s = 27\). Total distance between A and B = \((s+a) \times t\). \(= (54+27) \times 12\). \(= 81 \times 12\). \(= 972\ Kms\).

So, the Correct option is (D): \(972\ Kms\).