# Boat and Stream Aptitude Questions

(Q1) A man rows down a river 15 km in 3 hrs with the stream and returns in 15/2  hrs. The rate at which he rows in still water is:

(a) 2.5 kmph       (b) 1.5 kmph

(c) 3.5 kmph       (d) 4.5 kmph

Solution:
Downstream speed=x
Upstream Speed=y

Upstream Time=15/2  hrs
Downstream Time=3 hrs

Distance=15 km

x = Distance/downstream time = 15/3 = 5 km/hr
y = Distance/upstream time =15 / (15/2) = 2 km/hr

Speed of person = (x + y)/2 = (5 + 2)/2 = 3.5 km/hr

Option (c) is the right answer

(Q2) A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is

(a) 3:1                   (b) 4:3

(c) 1:2                    (d) 2:1

Let the speed of boat in still water=x kmph
Speed of current=y kmph

Downstream Rate= (x+y) kmph
Upstream Rate=(x-y) kmph

Distance=Speed × Time

=> (x – y) × 2t = (x + y) ×t
=> (x – y) × 2 =(x + y)
=> (x – y) × 2=(x + y)
=> 2x – 2y= x + y
=>2x – x= y + 2y
=> x = 3y
x : y = 3 : 1

option (a) is the right answer

(Q3). A man rows 12 km in 5 hours against the stream and the speed of current being  4 kmph. What time will be taken by him to row 15 km with the stream?

(a) 1 hr 27  min

(b) 1 hr 24  min

(c) 1 hr 25  min

(d) 1\ hour\ 26\frac{7}{13} \ minutes \\\ \\ Read Solution

Let x is speed of boat in still water
Speed of current=4 kmph

Distance=12 km

Upstream Speed=(x-4) kmph
Upstream Speed= Distance / Time

=> x – 4= 12/5
=> 5 (x-4) =12
=> 5x-20=12
=> x= 32/5
x=6.4 kmph

Downstream Speed=(x+y)
Downstream Speed=6.4 + 4

Downstream Speed=10.4 kmph

Time= Distance/Speed

Time= 15/10.4
Time= 1\ hour\ 26\frac{7}{13} \ minutes

Option (d) is the right answer

(Q4) A man rows to a place 60 km distance and back in 13 hours 30 minutes. He finds that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the Rate of the stream?

(a) 8 kmph          (b)  0.5 kmph

(c) 10 kmph        (d) 1 kmph

Let the speed of man is x kmph
Speed of stream=y kmph

Upstream Speed=(x-y) kmph
Downstream Speed=(x+y) kmph

Distance=60 km

Time= 27/2 hours

Distance/Downstream + Distance/Upstream Speed = Time

\frac{60}{x+y} \ +\ \frac{60}{x-y} \ =\ \frac{27}{2} \ \ \ \ \ \ \ \ \ \ ----eq( a)

Given that,
Downstream Distance= 5 km
Upstream Distance= 4 km

ATQ

\frac{Downstream\ Distance}{Downstream\ Speed} =\ \frac{Upstream\ Distance}{Upstream\ Speed} \ \ \ \ \ (as \ time\ is\ same) \\\ \\ \frac{5}{x+y} =\ \frac{4}{x-y}

==> 5 (x – y) = 4 ( x + y)
==> 5x – 5y = 4x + 4y
==> x = 9y

Put the value of x in equation ‘a’
\frac{60}{9y+y} +\frac{60}{9y-y} =\ \frac{27}{2}

On solving the above equation we get y=1 kmph

Option (d) is the right answer

(Q5). A boat running upstream takes 5 hours and 40 minutes to cover a certain distance, while it takes 3 hours to cover the same distance downstream. What is the ratio between the speed of the boat and speed of water current respectively?

(a) 13:4                 (b) 20:1

(c) 19:2                 (d) 1:19

Sol:
Let the speed of boat be x kmph
Speed of current = y kmph

Upstream rate = (x-y) kmph
Upstream Time= 5 hrs 40 min

Downstream rate = (x+y) kmph
Downstream time= 3 hrs

Distance=Time × Speed

According to question

(5+40/60) × (x-y) = 3 (x+y)

On solving we get
4x = 13y
x : y =13 : 4

Option (a) is the right answer

(Q6) .The speed of boat downstream is 15 km/hr and speed of current is 3 km/hr. Find the total time taken by the boat to cover 15 km upstream and 15 km downstream.

(a) 2 hours 40 minutes

(b) 2 hours 42 minutes

(c) 3 hours 10 minutes

(d) 2 hours 30 minutes

Distance = 15 km
Downstream Speed= 15 kmph
Speed of Current = 3kmph

Speed of boat in still water= Downstream Speed-Speed of current
Speed of boat in still water=15 – 2=12 kmph

Upstream Speed= Speed of boat in still water- Speed of Current
Upstream Speed=12 – 3 = 9 kmph

Upstream Time=Distance/Speed= 15/9 = 1 h 40 min
Downstream Time= Distance Speed =15/(12+3) =1 hour

Total Time = 2hr 40 min

Option (a) is the right answer

(Q7). A man rows to a place 35 km in distance and back in 10 hours 30 minutes. He found that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of flow of the stream.

(a) 1 km/hrs       (b) 0.75 km/hrs

(c) 1.33 km/hrs  (d) 1.5 km/hrs

Let the speed of man is x kmph
Speed of stream=y kmph

Upstream Speed=(x-y) kmph
Downstream Speed=(x+y) kmph

Distance=35 km
Time=10 hour 30 mins = 21/2  hours

(Distance/Downstream Speed) + (Distance/Upstream Speed) =Time

\frac{35}{x+y} +\frac{35}{x-y} =\ \frac{21}{2} \ \ \ \ \ \ \ \ \ \ .\ .\ .\ .\ eq( a)

Given that,
Downstream Distance= 5 km
Upstream Distance= 4 km

ATQ
\frac{Downstream\ Distance}{Downstream\ Speed} =\frac{Upstream\ Distance}{Upstream\ Speed} \ \ \ \ \ \ \ \ \ \ \ {Given\ that\ time\ is\ same} \\\ \\ \frac{5}{x+y} =\ \frac{4}{x-y} \ \ \ \ \ \ \ \ \

=> 5 (x – y) = 4 (x + y)
=> x = 9y

Put the value of x in equation ‘a’
\frac{35}{9y+y} +\frac{35}{9y-y} =\ \frac{21}{2} \ \ \ \ \ \ \

On solving the equation we get;
y=0.75 km/hr

Option (b) is the right answer

(08) The water in a river is flowing at the rate of 4 km/hr. If the width and depth of the river is 8m and 4m respectively, then how much water will enter the sea in 15 minutes.

(a) 60000 cu meter      (b) 18000 cu meter

(c) 28800 cu meter      (d) 32000 cu meter

If water Flows at 4kmph

So in 15 minutes it travels= 1 km=1000 m

Volume of water entering the sea in 15 minutes= Width×Depth×Distance

Volume of water entering the sea in 15 minutes=8×4×1000

Volume of water entering the sea in 15 minutes=32000 cu meter

option (d) is the right answer

(09) A boat goes 75 km upstream in 3 hours and 60 km downstream in 1.5 hours. Then the speed of the boat in still water is:

(a) 32.5 kmph    (b) 30 kmph

(c) 65 kmph        (d) 60 kmph

Upstream Distance= 75 km
Upstream Time= 3 hours

Downstream Distance= 60 km
Downstream Time=1.5 hours

Upstream Speed=Distance/Time= 75 / 3 =25 kmph

Downstream Speed= Distance/Time = 60/1.5 =40 kmph

Speed of boat in still water = (Upstream Speed + Downstream Speed) / 2

Speed of boat in still water= (25 + 40) /2=32.5 kmph

Option (a) is the right answer

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