Boats and Streams

1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
A. 8.5 km/hr	B. 10 km/hr.
C. 12.5 km/hr	D. 9 km/hr

Answer : Option B

Explanation :

Man's speed with the current = 15 km/hr

=>speed of the man + speed of the current = 15 km/hr

speed of the current is 2.5 km/hr

Hence, speed of the man = 15 - 2.5 = 12.5 km/hr

man's speed against the current = speed of the man - speed of the current

= 12.5 - 2.5 = 10 km/hr

2. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A. 10	B. 6
C. 5	D. 4

Answer : Option C

Time taken downstream = 30(15+v)

Time taken upstream = 30(15−v)

total time = 30(15+v)+30(15−v)

It is given that total time is 4 hours 30 minutes = 412 hour 
                                                                 = 92 houri.e., 30(15+v)+30(15−v)=92
⇒1(15+v)+1(15−v)=92×30=320

⇒15−v+15+v(15+v)(15−v)=320

⇒30152−v2=320⇒30225−v2=320

⇒10225−v2=120⇒225−v2=200

⇒v2=225−200=25

⇒v=5 km/hr