Two boats P and Q run between two cities A and B on a stream with flow of 5 km/h. The cities are 300 km apart and P and Q have still water speeds of 25 km/h and 15 km/h respectively. P and Q start from cities A and B towards B and A respectively at the same time. When and where will they meet for the second time?

Correct option is A

Given:

Speed of stream = 5km/h

Speed of boat P in still water = 25 km/h

Speed of boat Q in still water = 15 km/h

Distance between cities A and B = 300

Formula Used:

Effective speed of boat P downstream = Speed of boat P + Speed of stream

Effective speed of boat Q upstream = Speed of boat Q - Speed of stream

Relative speed of boats P and Q = Effective speed of boat P downstream} + Effective speed of boat Q upstream

Solution:

Speed of stream = 5 km/h

Distance = 300

When boat P goes from A to B then the speed of boat = 25+5 =30 km/h

And speed of Q = 15-5 = 10

Time taken by boat P to reached B = 300/30 = 10 hrs.

Distance covered by boat Q in 10 hrs. = 100 km.

Speed of boat P upstream = 25 – 5 = 20

Relative speed = 20 -10 =10 km/h

Time taken when they meet = 100/10 = 10 hrs.

Distance cover by Q in 10 hrs = 100 km

Total time when they meet second time = 10+10 = 20 hrs.

Distance from B = 100+100 = 200 km.

Hence the correct option is (a)