CAT 2023 Question Paper | Quant Slot 1

CAT Questions

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 14 : 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

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Video Explanation

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Explanatory Answer

Let the distance between city A and the meeting point M be D1 and the distance between city B and the meeting point M be D2.
Arvind covers D1 in t hours and D2 in 6 hours.
Speed of Arvind = \( \frac { D 1 } { t } = \frac { D 2 } { 6 } \)
\( \frac { D 1 } { D 2 } = \frac { t } { 6 } \)
Surbhi covers D1 in 24 hours and D2 in t hours.
Speed of Surbhi = \( \frac { D 1 } { 24 } = \frac { D 2 } { t } \)
\( \frac { D 1 } { D 2 } = \frac { 24 } { t } \)
\( \frac { D 1 } { D 2 } = \frac { t } { 6 } = \frac { 24 } { t } \)
t² = 6 × 24 = 12²
t = 12
Total time taken by Arvind to travel from city A to city B = (t + 6) = 18 hours.
Speed of Arvind = 54 kmph
Distance between city A to city B = 54 × 18 = 972 km.

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The answer is '972'