Explanation / Important formulas:
 Stream: Moving water of the river is called stream
 Still Water: If the water is not moving then it is called still water
 Downstream/Upstream: In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream
If the speed of a boat in still water is A km/hr and the speed of the stream is B km/hr, then:
 Speed downstream = (A + B) km/hr
 Speed upstream = (A – B) km/hr
If the speed downstream is x km/hr and the speed upstream is y km/hr, then:
 Speed in still water = ½(x+y) km/hr
 Rate of stream = ½(xy) km/hr
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Test  Boats and streams
Boats and streams  Question and Answers
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Question 1

A

2.5 kmph

B

3.5 kmph

C

7 kmph

D

23.5 kmph

b  s = 20
Solving the equations, s = 3.5 kmph
Question 2

A

10.5 km

B

24.5 km

C

17.5 km

D

20 km

= 3 km/hr
Distance travelled = speed * time
= 3*3.5 = 10.5 km
Question 3

A

2 kmph

B

3 kmph

C

4 kmph

D

5 kmph

Upstream speed = (7x) kmph
Downstream speed = (7+x) kmph
Time taken to travel upstream = (10/ (7x)) hrs
Time taken to travel upstream = (5/ (7+x)) hrs
(10/ (7x)) + (5/ (7+x)) = 3
3 x 2 + 5x – 42 = 0
Solving this equation, x= 3
Question 4

A

2 kmph

B

2.5 kmph

C

3 kmph

D

Data insufficient

9+x = 2*(9x)
X= 3
Question 5

A

12 kmph

B

9 kmph

C

2 kmph

D

10 kmph

(24/u) + (18/d) = 4.5
Solving, u = 8, d = 12
b = (u + d)/2 = 10 kmph
Question 6

A

4 hours

B

4.5 hours

C

5 hours

D

6 hours

S= d – b = 3
U = b – s = 12 kmph
Time taken to travel 72 km upstream
= 72/12 = 6 hours
Question 7

A

5:1

B

3: 2

C

4:1

D

2:3

D= 15 kmph
S= (d  u) / 2 = 2.5 kmph
B= (d + u)/2 = 12.5 kmph
b:s = 5:1
Question 8

A

8 kmph

B

4 kmph

C

2 kmph

D

6 kmph

d = 2u
s = (d  u)/2
Solving, s = 2 kmph
Question 9

A

15 km

B

10 km

C

3 km

D

5 km

Distance = 15 * 20/60 = 5 km
Question 10

A

45 km

B

22.5 km

C

36 km

D

36 km

U = 9 km/hr
D = 15 km/hr
(x/9) + (x/15) = 4
Distance = 22.5 km
Question 11

A

9 m/s

B

5 m/s

C

2 m/s

D

2.5 m/s

The options are given in m/s
9 kmph = (9*5/18) m/s = 2.5 m/s
Question 12

A

16 kmph

B

20 kmph

C

18 kmph

D

24 kmph

U = x – 4
D = x + 4
48/(x+4) = 32/(x4)
48x192 = 32x+128
16x = 320
X = 20 kmph
Question 13

A

20 km

B

25 km

C

24 km

D

18 km

U = b – s = 8 kmph
D = b + s = 12 kmph
(x/u) + (x/d) = 5
(x/8) + (x/12) = 5
Solving, x = 24 km
Question 14

A

3:1

B

2:1

C

1:2

D

3:2

b + s = 2(b  s)
b + s = 2b 2s
b = 3s
b:s = 3:1
Question 15

A

2.5 kmph

B

3 kmph

C

2 kmph

D

4 kmph

D = 15 kmph
S = (d  u)/2 = 3 kmph
Question 16

A

2.1 kmph

B

3 kmph

C

2.9 kmph

D

3.5 kmph

D = b + s
Average speed = 2ud/(u + d)
(2*7*d) / (7 + d) = 9.1
14d = 9.1(7 +d)
Solving, d = 13 kmph
S = d – u/2 = 3 kmph
Question 17

A

7:00 am

B

8:00 am

C

9:30 am

D

6:15 am

D = b + s = 10 kmph
Time taken to travel upstream = 30/6 = 5 hours
Time taken to travel downstream = 30/10 = 3 hours
Time in the island = 2hours
Total time = 10 hours
Therefore, the boat should have started at 7 in the morning
Question 18

A

3.5 kmph

B

3.25 kmph

C

3 kmph

D

6.5 kmph

D = 16.5 kmph
S = (d  u)/2 = 3 kmph
Question 19

A

3.5 hours

B

3.9 hours

C

4.5 hours

D

4 hours

D = 39/3 = 13 kmph
The man’s speed = u + d/2 = 10 kmph
He can cover a distance of 40 km in = 40/10 = 4 hours
Question 20

A

4 kmph

B

2 kmph

C

1 kmph

D

2.5 kmph

Upstream travel time = 16/u
Downstream travel time = 16/d
16/u + 16/d = 6
[16/ (6  s)] + [16/ (6+s)] = 6
Solving,
16(6 + s) + 16(6  s) = 6(36 – s2)
32*6 = 6(36 – s2)
S2 = 36  32 = 4
S = 2 kmph
Question 21

A

4.5 hours

B

3 hours

C

259 minutes

D

(7/9) hours

Time taken to travel 4.5km downstream = time taken for 3 km upstream
Speed is inversely proportional to time
Hence, 4.5*Upstream speed = 3*downstream speed
4.5u = 3d
4.5(b  s) = 3(b + s)
1.5b = 7.5s = 7.5*1.5
b = 7.5kmph
u = 6kmph
d = 9 kmph
Time taken to travel 10 km upstream = 10/u = 5/3
Time taken to travel 10 km downstream = 10/d = 10/9
Total time = 25/9 hours
= 2(7/9) hours
Question 22

A

6 kmph

B

5 kmph

C

4.5 kmph

D

7.5 kmph

Time taken to swim downstream = 5/(x 3)
Time taken to swim upstream = 3/(x+3)
[5/(x3)] + [3/(x+3)] = 2
5x+15+3x9 = 2(x29)
2x2 – 8x 24 = 0
X2 – 4x 12 = 0
(x6)(x+2) = 0
x can’t be 2
Hence, x = 6 kmph
Question 23

A

16.5 km

B

9 km

C

6 km

D

1.5 km

Downstream speed of the second boat = 18 kmph
In half an hour, distance travelled by first boat = 7.5 km
Distance travelled by second boat = 9 km
Distance between them = 1.5 km
Question 24

A

10.1 kmph

B

9.05 kmph

C

5.9 kmph

D

4.9 kmph

= 5.9 kmph
Question 25

A

1 hour

B

1.5 hours

C

150 minutes

D

180 minutes

Time taken = 15/10 = 1.5 hours
Question 26

A

12.5 kmph

B

8 kmph

C

3.5 kmph

D

7.5 kmph

Upstream speed = 20/2.5 = 8 kmph
Speed in still water = 8 + 4.5 = 12.5 kmph
Question 27

A

3 kmph

B

1.5 kmph

C

4.5 kmph

D

8.5 kmph

Time taken to travel 28 km upstream = 28/u
= 28/(xc) = 4
x – c = 28/4 = 7 (1)
Time taken to travel 40 km downstream = 40/(x + c) = 4
x + c = 40/4 = 10  (2)
Solving,
C = 1.5 kmph
Question 28

The current of a stream runs at the rate of 2.5 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 100 mins. Find the speed of the motor boat in still water?
A

15 kmph

B

12.5 kmph

C

10 kmph

D

7.5 kmph

Time taken to travel 10 km downstream = 10/ (b + s)
[10/ (b  2.5)] + [10/ (b + 2.5)] = 100/60
(b+2.5) + (b  2.5) = (1/6)*(b2  6.25)
b2  12b  6.25 = 0
(b 12.5) (b + 0.5) = 0
b = 12.5 kmph
Question 29

A

15 kmph

B

12 kmph

C

10 kmph

D

9 kmph

Time taken to travel 18 km upstream = 18/(b3)
[18/(b3)] – [18/(b+3)] = 30/60 (1)
18[(b+3) – (b  3)] = ½[b2  9]
36[6] = b2 – 9
b2 – 216 – 9 =0
b2 = 225
b = 15 kmph
To do quickly, we can substitute the option in equ(1)
Question 30

A

14 kmph

B

8 kmph

C

4 kmph

D

5 kmph

= (18  10) /2 = 4 kmph
Question 31

A

2 hours

B

3 hours

C

4 hours

D

5 hours

s = 4
d = b + s = 17
Time taken to go 68 km downstream = 68/17 = 4 hours
Question 32

A

1.2 km

B

1.8 km

C

2.4 km

D

3.6 km

S = 3
d = 15+3 = 18 kmph
t = 12 mins = 0.2 hours
Distance travelled downstream in 0.2 hours = 18*0.2
= 3.6 km
Question 33

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
A

160 km

B

180 km

C

200 km

D

200 km

B = 14
D = 18
U = 10
Let the distance between A and B be x
(x/18) + ((x/2)/10) = 19
10x+9x = 19*180
X = 180 km
Question 34

A

4 km/hr

B

6 km/hr

C

8 km/hr

D

Data inadequate

16/(b  s) = 4
b + s = 8
b – s = 4
Solving,
2b = 12
b = 6
Question 35

A

2.5 km/hr

B

4.2 km/hr

C

5 km/hr

D

10.5 km/hr

S = (du) /2 = 2.5 kmph
Question 36

A

3 kmph

B

4.5 kmph

C

9 kmph

D

18 kmph

Question 37

A

3 hrs

B

5 hrs

C

6 hrs

D

4.5 hrs

D = b + s
45/(b + s) = 3
B+s = 15
S = 3
U = b  s = 9
Time taken to travel 45 kms upstream = 45/9 = 5 hours
Question 38

A

23 km/hr

B

27 km/hr

C

25 km/hr

D

26 kmph

S = 3 kmph
B = u + s = 23 kmph
Question 39

A

4 km/hr

B

2 km/hr

C

3 km/hr

D

Data inadequate

D = 20/2 = 10 kmph
B – s= 4
B + s = 10
S = 3 kmph
Question 40

A

2

B

5

C

3

D

2.5

20/(b+s) = 12/(bs)
20*(10s) = 12*(10+s)
50 – 5s = 30 + 3s
8s = 20
S = 2.5
Question 41

A

2 hours

B

3 hours

C

4 hours

D

5 hours

S = 4
U = 9
Time taken to travel 45km upstream = 45/9 = 5 hours
Question 42

A

8.5 km/hr

B

9 km/hr

C

10 km/hr

D

12.5 km/hr

S = 2.5
Man’s speed = 15 – 2.5 = 12.5
Man’s speed against the current = 12.5 – 2.5 = 10 kmph
Question 43

A

2:1

B

3:2

C

8:3

D

Cannot be determined

8 hrs 48 mins
= 8 + (48/60)
= 8.8
x/(b  s) = 8.8
x/(b + s) = 4
8.8(b  s) = 4(b + s)
2.2b – 2.2s = b + s
1.2b = 3.2s
b:s = 8:3
Question 44

A

4

B

5

C

6

D

10

30/u + 30/d = 4.5
30/(15  s) + 30 /(15 + s) = 4.5
30*30 = 4.5(15  s) (15 + s)
200 = 225 – s2
s2 = 25
s = 5
Question 45

A

3 km/hr

B

5 km/hr

C

8 km/hr

D

9 km/ hr

b – s = 5
2b = 16
b = 8
Question 46

A

12 kmph

B

13 kmph

C

15 kmph

D

16 kmph

Let the distance be x km
x/(b+3) = 1
x/(b3) = 1.5
b + 3 = 1.5(b  3)
0.5b = 7.5
b = 15 kmph
Question 47

A

8.5 km/hr

B

9 km/hr

C

10 km/hr

D

12.5 km/hr

s = 3.5
Boy’s speed = 16 – 3.5 = 12.5
Boy’s speed against the current = 12.5 – 3.5 = 9 kmph
Question 48

A

1.2 km/hr

B

1.5 km/hr

C

1.6 km/hr

D

1.8 km/hr

Question 49

A

40 minutes

B

1 hour

C

1 hour 15 min

D

1 hour 30 min

1/d = 1/6
u = 2
d = 6
b = (u + d)/2 = 4
Time taken to travel 5 km in still water = 5/4
= 1.25 hours
= 1 hour 15 mins
Question 50

There is a road beside a river. Two friends, P and Q, started from a place A, moved to a temple situated at another place B and then returned to A again. P moves on a cycle at a speed of 12km/hr, while Q sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first?
A

P

B

Q

C

Both P and Q

D

Data inadequate

b = 10
s = 4
u = 6
d = 14
Q travels x km upstream at 6 kmph and x km downstream at 14 kmph
Q’s average speed = 2*14*6/20
= 8.4 kmph
Hence, P returns first
Question 51

A

7.5 km/hr

B

7 km/ hr

C

9 km/hr

D

8 km/hr

b + s = 15
s = 7 kmph
Question 52

A

20 mins

B

40 mins

C

30 mins

D

15 mins

u = 16
s = 4
d = 24
Time taken to travel 16 km downstream = 16/24
= 2/3 = 40 mins
Question 53

A

7 km/hr

B

8.5 km/hr

C

9 km/hr

D

None of these

Question 54

A boat running upstream takes 8 hours 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

3:1

D

3:1

x/(b  s) = 8
x/(b + s) = 4
8(b  s) = 4(b + s)
2b – 2s = b + s
b = 3s
b:s = 3:1
Question 55

A

1. 2 km

B

1.8 km

C

2.4 km

D

3.6 km

s = 3
d = 18
Distance in 12 mins = 18*12/60
= 3.6 km
Question 56

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

36/(10  s) – 36/(10 + s) = 90/60
36*2s = 1.5*(100 – s2)
100 – s2 = 72s /1.5
s2 + 48s – 100 = 0
(s  2) (s + 50) = 0
s = 2
Question 57

A

2.4 km

B

2.5 km

C

3 km

D

3.6 km

U = 4, d = 6
x/4 + x/6 = 1
5x = 12
X = 2.4
Question 58

A boat covers a certain distance upstream in 1 hour 30 minutes, while it comes back in 1 hour. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?
A

12 kmph

B

13 kmph

C

14 kmph

D

15 kmph

x/(b3) = 1.5
x/(b+3) = 1
1.5(b3) = b+3
0.5b = 7.5
b = 15
Question 59

A

3

B

5

C

8

D

9

u = 5
b = (u + d)/2 = 8
Question 60

A

2

B

3

C

4

D

5

= 4 kmph
b = 5 kmph
Question 61

A

4.25 kmph

B

6 kmph

C

6.5 kmph

D

8.5 kmph

u = 3.5
s = 1.5
d = 6.5 kmph
Question 62

Speed of a boat is standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at the distance of 105 km and comes back to the starting point. The total time taken by him is
A

16 hours

B

18 hours

C

20 hours

D

24 hours

s = 1.5
u = 7.5
d = 10.5
Time taken = (105/10.5) + (105/7.5)
= 10 + 14 = 24 hours
Question 63

The effective speed of travel of a boat downstream is 20 kmph whereas it is 10 kmph upstream. What is the speed of the current in kmph?
A

2

B

7

C

5

D

6

u = 10
s = (d  u)/2 = 5 kmph
Question 64

A

6.5 km/hr

B

7 km/hr

C

5 km/hr

D

None of these

u = 3
b = (7+3)/2 = 5
Question 65

A

10 seconds

B

15 seconds

C

20 seconds

D

12 seconds

= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds
Question 66

A

32 km

B

25 km

C

28 km

D

None of these

Total time = x/(9+1) + x/(91) = 4.5
x/10 + x/8 = 9/2
(4x + 5x) /40
9/2
X = 20 km
Question 67

A

13, 3

B

12, 6

C

14, 4

D

15, 3

Given x + y = 18  (1)
And x  y = 10  (2)
From (1) & (2) 2x = 28
X = 14, y = 4
Question 68

A

15 kmph

B

10 kmph

C

12 kmph

D

12.5 kmph

Now 30/(a + b) + 20/(a  b) = 4 and
45/(a + b) + 40/(a  b) = 7
Solving the equation,
The speed of man in still water is 12.5 kmph
Question 69

A

12 kmph

B

13 kmph

C

14 kmph

D

15 kmph

The ratio of the speed of the boat in still water to the speed of the stream.
= (2+1) / (21) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph
Question 70

A

70, 10 kmph

B

35, 27 kmph

C

50, 60 kmph

D

45, 55 kmph

Speed of the stream = (8060) /2 = 10 kmph
Question 71

A

8 kmph

B

4 kmph

C

2 kmph

D

10 kmph

S = 1.5
DS = 6
US = 3
AS = (2*6*3) /9 = 4
Question 72

A

35, 25 kmph

B

80, 40 kmph

C

40, 60 kmph

D

50, 55 kmph

Speed upstream = 60 – 20 = 40 kmph
Question 73

A

2 kmph

B

8 kmph

C

16 kmph

D

4 kmph

? 1
18  3 US = 6
? 1 M = ?
M = (10 + 6) /2 = 8
Question 74

A

10 kmph

B

5 kmph

C

20 kmph

D

22 kmph

S = 5
DS = 15 + 5 = 20
Question 75

A

13 hr

B

12.5 hr

C

11 hr

D

12 hr

Speed downstream = (6+2) = 8 km/hr
Speed upstream = (62) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken = Time taken downstream + Time taken upstream
= (32/8) + (32/4) = (32/8) + (64/8) = 96/8 = 12 hr
Question 76

A

3/1 km/hr

B

2/3 km/hr

C

2/1 km/hr

D

½ km/hr

Speed downstream = 3/(18/60) = 10 km/hr
Rate of current = (109)/2 = ½ km/hr
Question 77

A

18.57 km

B

18.75 km

C

51.87 km

D

51.78 km

Speed upstream = (40  10) = 30 kmph
Speed downstream = (40 +10) = 50 kmph
Total time taken = 1 hr
(x/50) + (x/30) = 1
8x/150 = 1
x = 150/8
x = 18.75 km
Question 78

A

2.5 hrs

B

4 hrs

C

3 hrs

D

2 hrs

Speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed = 54/27 = 2 hours
Question 79

A

8 kmph

B

6 kmph

C

7 kmph

D

9 kmph

Question 80

A

10 kmph

B

15 kmph

C

12 kmph

D

14 kmph

Speed downstream = (x+3) kmph
Speed upstream = (x3) kmph
(x+3) x 1 = (x – 3) x 3/2
2x + 6 = 3x – 9
x = 15 kmph
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