Multiple choice

[CAT 1994] A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

  1. 25 km

  2. 22.5 km

  3. 24 km

  4. 20 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time for B to reach Y = 27 / 7 hours. In that time, A travels 5 * (27/7) = 135/7 km. B turns back and meets A at Z. Let t be the time after B reaches Y. (5 + 7) * t = distance B traveled back = 27 - 135/7 = 54/7. t = 54/84 = 9/14 hours. Distance from X to Z = A's total distance = 5 * (27/7 + 9/14) = 5 * (54/14 + 9/14) = 5 * (63/14) = 5 * 4.5 = 22.5 km.

AI explanation

Let the two walkers meet after time t hours. Using the relative speed concept for motion in opposite directions, the combined speed of A and B is 5 kmph plus 7 kmph, which equals 12 kmph. Since they meet after covering the 27 km distance between them twice, the total relative distance is 54 km, making the time t equal to 54 divided by 12, or 4.5 hours. The distance from X to Z is the distance A walks in this time, which is 5 kmph multiplied by 4.5 hours, equaling 22.5 km.

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