NinetynineCAT 2022 Slot 2 QA Q22 Time, Speed & Distance
Question 22 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.
Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is
- A12
- B18
- C20
- D24
Answer: (B) 18 Time, Speed & Distance MCQ
Solution
- The paths are perpendicular. After 2 hours the distances are \(2v\) and \(2(v+6)\).
- \(4v^2+4(v+6)^2=3600\Rightarrow v^2+(v+6)^2=900\).
- \(v=18\): \(324+576=900\).
Shortcut. 18-24-30 is a 3-4-5 triple scaled by 6.