CAT 2022 Slot 3 QA Q21 Time, Speed & Distance

Question 21 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be
  1. A
    8
  2. B
    12
  3. C
    6
  4. D
    4

Answer: (B) 12 Time, Speed & Distance MCQ

Solution

  1. Both ships start 24 km from the port, with a \(60^\circ\) angle at the port. The slower ship is then 16 km away; let the faster be \(f\) km away.
  2. Right angle at the slower ship would need \(16=f\cos60^\circ\), i.e. \(f=32\gt24\): impossible. So the right angle is at the faster ship: \(f=16\cos60^\circ=8\).
  3. The faster ship covered 16 km while the slower covered 8, so speeds are in ratio 2:1.
  4. When the faster covers 24 km, the slower covers 12 km, leaving \(24-12=12\) km.

More Time, Speed & Distance questions from CAT

All 48 Time, Speed & Distance questions asked since 2017.