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Relative Speed and Time Difference

CAT 2024 Slot 1 · Quantitative Ability · Medium · Speed Time Distance

This is a medium Quantitative Ability question from the CAT 2024 Slot 1 paper. It tests Speed Time Distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

  1. A.

    16

  2. B.

    14

  3. C.

    12

  4. D.

    18

Answer

C

Explanation

Distance = 45 km. Crossing time = 1.5 hours. Combined speed vA+vS=451.5=30v_A + v_S = \frac{45}{1.5} = 30 km/h. Time taken by Anil tA=45vAt_A = \frac{45}{v_A}, and Sunil tS=45vSt_S = \frac{45}{v_S}.

Given tA−tS=1.25=54t_A - t_S = 1.25 = \frac{5}{4} hours: 45vA−4530−vA=54\frac{45}{v_A} - \frac{45}{30 - v_A} = \frac{5}{4} 9vA−930−vA=14\frac{9}{v_A} - \frac{9}{30 - v_A} = \frac{1}{4} 36(30−2vA)=vA(30−vA)36(30 - 2v_A) = v_A(30 - v_A) vA2−102vA+1080=0v_A^2 - 102v_A + 1080 = 0 (vA−12)(vA−90)=0(v_A - 12)(v_A - 90) = 0 Since vA<30v_A < 30, vA=12v_A = 12 km/h.

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