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The distance between two places X and Y is 60 km. A and B move from X to Y at 16 km/h and 20 km/h, respectively. B reaches Y and immediately turns back and meets A at Z (some place between X and Y). What is the distance (in km) between X and Z?

  • A.\(52\frac{1}{2}\)
  • B.\(52\frac{1}{4}\)
  • C.\(53\frac{1}{3}\)
  • D.\(55\frac{2}{3}\)

Answer: C

XZ is 53 1/3 km. A and B start together from X. B reaches Y after \[\frac{60}{20} = 3\] hours, by which time A has covered 16 x 3 = 48 km, so A is 12 km from Y. B now comes back towards A and they approach each other at 16 + 20 = 36 km/h. They meet after \[\frac{12}{36} = \frac{1}{3}\] hour, in which A goes a further 16/3 = 5 1/3 km. Hence \[XZ = 48 + 5\tfrac{1}{3} = 53\tfrac{1}{3}\] km. The other options, 52 1/2, 52 1/4 and 55 2/3, do not satisfy these distances.

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