Question

Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is [This question was asked as TITA]

• A. 982 Kms
• B. 970 Kms
• C. 974 Kms
• D. 972 Kms

Answer 1

Answer: (D)

972 Kms

Answer 2

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): $972\ Kms$.