Boats and Streams Problems with Detailed Solution
Question No: 01
A boat goes
16 km upstream in 2 hours and downstream in 1 hour. Find how time this boat
will take to travel 32 km in all still water?
(A) 1.5
hours
(B) 2 hours
(C) 2 hours
40 minutes
(D) 2.5
hours
Answer:
Option C
Solution:
Speed in upstream
= 16/2 kmph = 8 kmph
Speed in downstream = 16 kmph
Speed of
boat in still water = 1/2(Speed in upstream + Speed in downstream)
=1/2 (16 + 8) kmph
= 12 kmph
(Or),
x + y = 16/1
=16......... (eq. 1)
x - y = 16/1
= 8..........(eq. 2)
Adding
equation (1) and equation (2), we get,
x=12 kmph
Therefore,
time taken by the boat to travel 32 km is,
t = 32/12
= 2 hrs 40 min.
Question No: 02
A man goes
by motor boat a certain distance upstream at 15 kmph and returns the same
downstream at 20 kmph. The total time taken for the journey was 7 hrs. Find how
far did he go?
(A) 30 km
(B) 60 km
(C) 90 km
(D) 120 km
Answer:
Option B
Solution:
If the boat goes
a certain distance ‘d’ downstream and returns upstream and total time taken be ‘t’, then t =
{d/(x - y)} + {d/(x + y)} = = (d/upstream) + (d/downstream)
Therefore, 7
= (d/15) + (d/20)
=> d = 60 km.
Question No: 03
A man can
row 5 km per hr in still water. If the river is flowing at 1 km per hr, it
takes him 75 minutes to row to a place and back. How far is the place?
(A) 2.5 km
(B) 3 km
(C) 3.5 km
(D) 4.5 km
Answer:
Option B
Solution:
If the boat
goes a certain distance ‘d’ downstream and returns upstream and total time taken be ‘t’, then t =
{d/(x - y)} + {d/(x + y)}
75 min = 75/60 hrs
Therefore,
75/60 = {d /(5 + 1)} + {d/ (5 - 1)}
=> 5/4 = (2d + 3d)/12
=> d = 3 km.
Question No. 04
A boat
running upstream takes 8 hours 48 minutes to cover a certain distance, while it
takes 4 hours to cover the same distance running downstream. What is the ratio
between the speed of the boat and speed of the water current respectively?
(A) 2 : 1
(B) 3 : 2
(C) 8 : 3
(D) None of
these
Answer:
Option C
Solution:
Let the
man's rate upstream be ‘x’ kmph and that downstream be ‘y’ kmph.
Then,
distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4
hrs.
=> (x ×
8 ^{4}/_{5}) = (y × 4)
=> 44x/5 = 4y
=> y = 11x/5
∴ Required
ratio = (y + x)/2 : (y - x)/2
= [(16x/5) × (1/2)] : [(6x/5) × (1/2)]
= 8/5 : 3/5
= 8 : 3
Question No. 05
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) 4
(B) 5
(C) 6
(D) 10
Answer:
Option B
Solution:
Let the
speed of the stream be x km/hr. Then,
Speed
downstream = (15 + x) km/hr,
Speed
upstream = (15 - x) km/hr.
∴ {30/(15
+ x)} + {30/(15 - x)} = 4½
=> 900/(225 - x²) = 9/2
=> 9x^{2} =
225
=> x^{2} =
25
=> x =
5 km/hr.
Question No. 06
A boat takes
90 minutes less to travel 36 miles downstream than to travel the same distance
upstream. If the speed of the boat in still water is 10 mph, the speed of the
stream is:
(A) 2 mph
(B) 2.5 mph
(C) 3 mph
(D) 4 mph
Answer:
Option A
Solution:
Let the
speed of the stream x mph. Then,
Speed
downstream = (10 + x) mph,
Speed
upstream = (10 - x) mph.
∴ {36/(10
- x)} - {36/(10 - x)} = 90/60
=> 72x x 60 = 90 (100
- x^{2})
=> x^{2} + 48x -
100 = 0
=> (x + 50)(x - 2) =
0
=> x = 2 mph.
Question No. 07
A man can
row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes
him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.5 km
(C) 3 km
(D) 3.6 km
Answer:
Option A
Solution:
Speed
downstream = (5 + 1) kmph = 6 kmph.
Speed
upstream = (5 - 1) kmph = 4 kmph.
Let the
required distance be x km.
Then, (x/6) + (x/4) = 1
=> 2x + 3x = 12
=>5x =
12
=> x =
2.4 km.
Question No. 08
A man can
row three-quarters of a kilometer against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man
in still water is:
(A) 2
(B) 3
(C) 4
(D) 5
Answer:
Option D
Solution:
We can write
three-quarters of a kilometer as 750 meters, and 11¼ minutes as 675 seconds.
Rate
upstream = (750/675) m/sec = (10/9) m/sec
Rate
downstream = (750/450) m/sec = (5/3) m/sec
∴ Rate
in still water = ½ {(10/9) + (5/3)} m/sec
= (25/18)
m/sec
= {(25/18) × (18/5)} km/hr
= 5 km/hr
Question No. 09
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) 3 : 2
(D) 4 : 3
Answer:
Option B
Solution:
Let man's
rate upstream be x kmph.
Then, his
rate downstream = 2x kmph.
∴ (Speed
in still water) : (Speed of stream) = {(2x + x)/2} : {(2x - x)/2}
= (3x/2) : (x/2)
= 3 : 1
Question No. 10
A man rows
to a place 48 km distant and come back in 14 hours. He finds that he can row 4
km with the stream in the same time as 3 km against the stream. The rate of the
stream is:
(A) 1 km/hr
(B) 1.5
km/hr
(C) 2 km/hr
(D) 2.5
km/hr
Answer:
Option A
Solution:
Suppose he
move 4 km downstream in x hours. Then,
Speed downstream
= (4/x) km/hr
Speed
upstream = (3/x) km/hr
∴ {48/(4/x)} + {48/(3/x)} = 14 or x = ½
So, Speed
downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the
stream = ½ (8 - 6) km/hr = 1 km/hr.
Boats and Streams:
Formula: Boats and Streams Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01
Formula: Boats and Streams Formulas
Solved Examples: Solved Examples: Set 01
Practice Test: Practice Test: 01
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