Multiple choice

Three persons A, B and C have to travel from place P to place Q. A's speed is 30 km/hr, whereas the speed of B is 33.33% less than C's speed as well as 11.11% less than average value of speeds of A and C. A starts from point P 2 hrs earlier than B, and C starts from point P y hrs after A. If all three of them reach at the same point after some time, then y is

  1. 4.5

  2. 4

  3. 3.5

  4. None of these

  5. This situation is impossible.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C's speed be v. B's speed is (2/3)v. Also, B's speed is (8/9) * ((30+v)/2). Solving (2/3)v = (4/9)(30+v) gives 6v = 120 + 4v, so 2v = 120, v = 60 km/hr. B's speed is 40 km/hr. A travels at 30 km/hr. For them to meet at the same point, the time taken by each must align with their start times. Solving the relative time equations yields y = 4.

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