CAT 2023 Slot 1 Solved Paper

Question : 58 of 66

Marks: +1, -0

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

Your Answer:

Validate

Solution:

Let us assume the speeds of Arvind and Surbhi are 'a' and 's', respectively.
Let us say they meet after '

t

' hours
⇒ Arvind travelled s*t distance in

6 {\hrs}

and Surbhi travelled

{\a}^{⋆ t}

24 {\hrs}

⇒ {\ s}^* {\t}= {\a}^* 6

and

{\a}^* {\t}= {\ s}^{⋆ 24}⇒t^2=6 × 24⇒ {\t}=12

Given

a=54⇒s^{⋆} 12=54^{⋆} 6⇒s=27

.
⇒ Total distance between A and B is

( {\ s}+ {\a})^{⋆ {\t}}=(54+27)^{⋆} 12=81^{⋆} 12=972 {\Kms}

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