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: (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: (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: (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: (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: (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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