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

To solve this problem, let's denote the distance Arvind and Surbhi have traveled to meet each other as \(x\) km from their respective starting points.

Given that Arvind travels at a speed of 54 km/h, he takes 6 hours to cover the remaining distance after meeting Surbhi. Therefore, the remaining distance Arvind travels is:

\[ \text{Distance}_{\text{remaining\_Arvind}} = 54 \text{ km/h} \times 6 \text{ h} = 324 \text{ km} \]

Thus, this implies:

\[ x = \text{Total Distance} - 324 \]

Similarly, Surbhi takes 24 hours to cover the remaining distance after meeting Arvind. Let Surbhi's speed be \(v\) km/h. Then the distance she travels after meeting Arvind is:

\[ \text{Distance}_{\text{remaining\_Surbhi}} = v \text{ km/h} \times 24 \text{ h} \]

According to the problem, both Arvind and Surbhi meet at the same point, meaning Arvind's \(x\) km and Surbhi's total distance to meet Arvind after this is used in the equation:

\[ x + v \times 24 \text{ h} = \text{Total Distance} \]

Since Arvind and Surbhi meet exactly halfway in terms of time spent, Surbhi would take four times as long to complete her remaining journey as Arvind does:

\[ \frac{v}{54} = \frac{1}{4} \]

Thus, the speed of Surbhi is:

\[ v = \frac{54}{4} = 13.5 \text{ km/h} \]

Now apply this to Surbhi's remaining distance:

\[ \text{Distance}_{\text{remaining\_Surbhi}} = 13.5 \text{ km/h} \times 24 \text{ h} = 324 \text{ km} \]

Thus:

\[ \text{Total Distance} = 324 \text{ km} + 324 \text{ km} = 972 \text{ km} \]

Therefore, the distance between town A and town B is 972 km.