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 the speeds of Arvind be $a$ and speeds of Surbhi be $s$.
Let they meet after $t$ hours.
Arvind travelled $s×t$ distance in $6$ hrs and Surbhi travelled $a×t$ distance in $24$ hrs
$⇒s×t = a×6$
and $a×t = s×24$
$⇒t^2 = 6 × 24$
$⇒t^2 =144$
$⇒t=\sqrt {144}$
$⇒t=12$
Given that, $a = 54$
$⇒ s \times 12 = 54\times6$
$⇒ s = \frac {54\times6}{12}$
$⇒ s = 27$
Total distance between $A$ & $B$,
$=(s+a)×t$
$= (54+27)×12$
$= 81×12$
$= 972\ Kms$

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