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Question

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?

CAT 2021

A
B
C
D
7.5 hours and 20 hours
Solution

Correct option is

(D)

When boat P travels downstream, it will effectively have a speed to 30kmph. similarly, Q will have an effective speed of 10kmph. The relative speed = 40kmph. So, the two boats will meet for the first time after 300/40 hours (Distance/relative speed) = 7.5 hours

now, The second part , 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 (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 traveling upstream

P’s speed = 20km/hr

Q’s speed = 10 km/hr => Relative speed = 10kmph

Q is ahead of P by 100 kms

P will catch up with Q after 10 more hours (Relative Distance/relative speed – 100/10).

So, P and Q will meet after 20 hours at a point 200 kms from city B