CAT 2023 Slot 1 QA Q14 Time, Speed & Distance

Question 14 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 972 Time, Speed & Distance TITA

Solution

After meeting, times are 6 h and 24 h, so \(\frac{v_A}{v_S} = \sqrt{\frac{24}{6}} = 2\); Surbhi's speed is 27 km/h.
After meeting, Arvind covers \(54\times6 = 324\) km, which is exactly what Surbhi had covered before meeting.
Time to meet \(= \frac{324}{27} = 12\) h, in which Arvind covers \(54\times12 = 648\) km.
Distance \(AB = 648 + 324 = 972\) km.

Shortcut. Meeting time \(= \sqrt{6\times24} = 12\) h; total time for Arvind \(= 18\) h, so \(54\times18 = 972\).