A motorboat, whose speed in 15 km/h in still water goes 50 km downstream and comes back in a total of 7 hours 30 minutes. The speed of the stream (in km/h) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5.
Let the speed of the stream be x km/h.
Downstream speed = Speed of boat in still water + Speed of stream
⇒ (15 + x) km/h
Upstream speed = Speed of boat in still water - Speed of stream
⇒ (15 - x) km/h
Total distance = Speed × Time
According to the given question,
50/(15 + x) + 50/(15 - x) = 7.5
⇒ 50(15 - x) + 50(15 + x) = 7.5(15 + x)(15 - x)
⇒ 750 - 50x + 750 + 50x = 7.5(225 - x2)
⇒ 1687.5 - 7.5x2 = 1500
⇒ 7.5x2 = 187.5
⇒ x2 = 25
⇒ x = 5