# Boats & Streams Model Questions Set 1 Practice Questions Answers Test With Solutions & More Shortcuts

#### BOATS & STREAMS PRACTICE TEST [1 - EXERCISES]

Question : 1

The speed of a motor boat to that of the current of water is 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in

a) 6 hours 30 min

b) 5 hours

c) 6 hours 15 min

d) 6 hours 50 min

Let speed of boat = 36x km/h

Speed of current = 5x km/h

∴ \$(36x + 5x) × 310/60=(36x-5x) × t\$

\$t={41×310}/{60×31}=41/6\$= 6H 50 min

Question : 2

The speed of a boat in still water is 8 km/hr. It can travel 20 km downstream at the same time as it can travel 12 km upstream, the rate of stream (in kmph) is

a) 2.5

b) 0.5

c) 2

d) 2.75

Let rate of stream = x kmph

∴ \$20/{8+x}=12/{8-x}\$

160 – 20x = 96 + 12x

64 = 32x

x = 2

∴ Rate of stream = 2 kmph

Question : 3

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is

a) 2 : 1

b) 3 : 1

c) 4 : 3

d) 3 : 2

Let speed in downstream = (x + y)

Speed in upstream = (x – y)

∴ (x + y) = 2 (x – y)

x = 3y

x : y = 3 : 1

Question : 4

If a man’s rate with the current is 12 km/hr. and the rate of the current is 1.5 km/hr, then man’s rate against the current is –

a) 5.25 km/hr

b) 9 km/hr

c) 6.75 km/hr

d) 7.5 km/hr

Let the rate against the current be x km/hr. Then,

\${12-x}/2\$ = 1.5 ⇒12 – x = 3 ⇒ x = 9 km / hr

Question : 5

A man rows a distance downstream in 45 min and the same distance upstream in 75 min. What is the ratio of speed of the stream to the boat in still water ?

a) 1 : 4

b) 1 : 2

c) 1 : 3

d) 2 : 3

Let speed of boat in still water = x km/hr

Let speed of stream = y km/hr

Let distance covered = d km

∴ \$d/{x+y}=45/60=3/4\$ …(1)

\$d/{x-y}=75/60=5/4\$ …(2)

Form (1) & (2),

\${x-y}/{x+y}=3/5 ⇒5x-5y=3x+3y\$

⇒2x=8y ⇒ \$y/x=1/4 \$

∴ ratio of speed of the stream to boat in still water = 1 : 4

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