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?
Effective speed of boat P (starting from city A) = 25+5 = 30 km/hr (downstream)
Effective speed of boat Q (starting from city B) = 15-5 = 10 km/hr (upstream)
Boat P is faster. i.e. P reaches city B in $$ \frac{300}{30} $$ = 10 hrs.
In 10 hrs, Q travels 10 x 10 = 100 km (from city B)
After 10hrs, P travels upstream. Effective speed of P = 25 - 5 = 20 km/hr
Effective speed of Q = 10 km/hr
Let the boats meet after time t and at a distance s from city B
Distance to be travelled by P = s
Distance to be travelled by Q = s - 100
Equating time taken by PÂ and Q,Â
$$ \frac{s}{20} =Â Â \frac{s-100}{10} $$
2(s - 100) = sÂ
i.e. s = 200 km
t = 10 +Â $$ \frac{200}{20} $$ = 20hrs
The boats will meet 2nd time after 20hrs, 200km from city B.
Therefore, Option D is correct.
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