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Meeting Time and Distance Formula

CAT 2023 Slot 1 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

Answer

972

Explanation

Let vAv_A and vSv_S be the speeds of Arvind and Surbhi, and tA,tSt_A, t_S be the times taken after meeting. By the standard result: vAvS=tStA=246=2\frac{v_A}{v_S} = \sqrt{\frac{t_S}{t_A}} = \sqrt{\frac{24}{6}} = 2 Since vA=54v_A = 54 km/h, vS=542=27v_S = \frac{54}{2} = 27 km/h.

The time taken until they meet is t=tAtS=6×24=12t = \sqrt{t_A t_S} = \sqrt{6 \times 24} = 12 hours.

Total distance between A and B =(vA+vS)×t=(54+27)×12=81×12=972= (v_A + v_S) \times t = (54 + 27) \times 12 = 81 \times 12 = 972 km.

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