Boats & Streams Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Boats & Streams PRACTICE TEST [1 - EXERCISES]
Boats & Streams Model Questions Set 1
Question : 16
A man rows 10 km upstream and back again to the starting point in 55 min. If the speed of stream is 2 km/hr, then the speed of rowing in still water is
a) 21 km/hr
b) 22 km/hr
c) 19 km/hr
d) 25 km/hr
Answer »Answer: (b)
Let speed in still water = x km/h
Speed of stream = 2km/h
∴ $10/{x+2}+10/{x-2}=55/60$
$10x+10x=11/12(x^2-4)$
$11x^2-240x-44=0$
x = 22
∴ speed in still water = 22 km/h
Question : 17
A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $6{1/2}$ hour. The velocity of the current is
a) 3 km/hr
b) 2.4 km/hr
c) 2 km/hr
d) 0.75 km/hr
Answer »Answer: (c)
Let upstream rate = x km/hr,
downstream rate = y km/hr
∴ $24/x+36/y=6$ ...(1)
$36/x+24/y=13/2$ ...(2)
Add (1) and (2) , we get
$60{(1/x+1/y)}=25/2 ⇒ 1/x+1/y=5/24$ ...(3)
Subtract (1) from (2)
$12{(1/x-1/y)}=1/2 ⇒ 1/x-1/y=1/24$ ...(4)
Add (3) and (4)
$2/x=6/24⇒x=8$
rom (3) y = 12
∴ Velocity of current = $1/2{(y-x)}=1/2{(12-8)}$=2km/hr
Question : 18
A man can row a boat 120 km with stream in 5 hours. If speed of the boat is double the speed of the stream, then the speed of stream is
a) 9 km/h
b) 6 km/h
c) 8 km/h
d) 12 km/h
Answer »Answer: (c)
Speed of the boat downstream =$120/5$ = 24 km/h
Ratio of speeds of boat and stream = 2 : 1
∴ Speed of the stream = $1/3×24$ = 8 km/h
Question : 19
A man can row three-quarters of a kilometer against the water stream in $11{1/4}$ minutes and along the stream in $7{1/2}$ minutes respectively. The speed in (km/hr) of the man in still water is
a) 5
b) 3.5
c) 2.5
d) 6.5
Answer »Answer: (a)
Question : 20
A man can row 5 kmph in the still water. If the river is running at 2 kmph, it takes him 5 hours to row up to a place and come down. How far is the place?
a) 10 km
b) 6 km
c) 8 km
d) 14 km
Answer »Answer: (c)
Let the distance = d km
Time taken to row upstream '$t_1$ ' = $d/{5-3}=d/2$ …(1)
Time taken to row downstream $'t_2 '$ = $d/{5+3}=d/8$ …(2)
$t_1 + t_2$ = 5 (Given)
∴ $d/2+ d/8 = 5$
⇒ ${4d+d}/8=5⇒ d=8km $
∴ Distance of the place = 8 km.
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