CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

The question is from the topic Boats and Streams. It discusses about two boats with different speeds roaming between two cities on a stream. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 10: City A to City B is a downstream journey on a stream which flows at a speed of 5km/hr. Boats P and Q run a shuttle service between the two cities that are 300 kms apart. Boat P, which starts from City A has a still-water speed of 25km/hr, while boat Q, which starts from city B at the same time has a still-water speed of 15km/hr. When will the two boats meet for the first time? (this part is easy) When and where will they meet for the second time?

1. 7.5 hours and 15 hours
2. 7.5 hours and 18 hours
3. 8 hours and 18 hours
4. 7.5 hours and 20 hours

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Understanding relative speed would help.

Boat P starts from city A and Q starts from city B.
When boat P travels downstream, it will effectively have a speed to 30kmph. Likewise, Q will have an effective speed of 10kmph. The relative speed = 40kmph. So, the two boats will meet for the first time after \\frac{300}{40}\\) hours (Distance/relative speed) = 7.5 hours (Actually, for this part we do not need the speed of the stream)
The second part is more interesting, because the speed of the boats change when they change direction. Boat P is quicker, so it will reach the destination sooner. Boat P will reach City B in 10 hours \\frac{300}{30}\\). When boat P reaches city B, boat Q will be at a point 100kms from city B.

After 10 hours, both P and Q will be travelling upstream,
P's speed = 20 km/hr
Q's speed = 10 km/hr
Relative speed = 10km/hr
Q is ahead of P by 100 kms

P will catch up with Q after 10 more hours \\frac{Distance}{RelativeSpeed}\\) − \\frac{100}{10}\\).
So, P and Q will meet after 20 hours at a point 200 kms from city B

The question is " When will the two boats meet for the first time? When and where will they meet for the second time?"

Hence, the answer is 7.5 hours and 20 hours

Choice D is the correct answer.