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

The Correct Option is D

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): \(972\ Kms\).