Sunday, 21 February 2016

Aptitude Questions - Boats and Streams - Solved Questions

Aptitude for CAT, GMAT , Bank Tests, Campus Placements
Solved problems on Boats and Streams:
1.    If the speed of a boat in still water is 14 kmph and the rate of stream is 4 kmph. Find the upstream speed and downstream speed of the boat?
a)10 kmph & 18 kmph    b)18 kmph &  kmph     
c)16 kmph & 8 kmph     d)7 kmph & 12 kmph
Answer : A
Explanation :
Given that speed of boat x= 14 kmph
                                     Speed of stream y= 4 kmph
     $\therefore$ Upstream speed    = (x - y) = 14 -4 = 10 kmph
     $\therefore$ Downstream speed = (x + y)= 14+4 = 18 kmph

2.    The speed of man in still water is 12 kmph. What will be his speed with the stream, if his speed in upstream is 8 kmph?
         a)     9 kmph      b) 11 kmph     c)14 kmph     d)16 kmph    
Answer: D
Explanation:
Given that, speed of the man in still water= 12 kmph
Upstream speed of the man (x-y)=8 kmph =>(12-y)=8
            $\therefore$ speed of the stream y=4 kmph
      Speed downstream =(x+y)=(12+4)= 16 kmph

3.     Sharma can row upstream at 14 kmph and downstream at 8 kmph. Find the Sharma’s rate in still water and the speed of the current?
a)11kmph , 3 kmph          b)12 kmph,6 kmph  
c)11 kmph, 6 kmph          d)14 kmph , 5 kmph
Answer : A
Explanation :
According to formula (4),Speed of Sharma in still water                           =$\frac{(Downstream\:Speed\:+Upstream\:Speed)}{2}$
                             = $\frac{1}{2}$ (14+8) = $\frac{22}{2}$ = 11 kmph
 Speed of the current = $ \frac{(Downstream\:Speed\:- Upstream\:Speed)}{2}$
                            =$ \frac{1}{2}$ (14-8) = $\frac{6}{2}$ = 3 kmph

4.    A man can row 40 km downstream and 24 km upstream, taking 8 hours each time. What Is the speed of the stream?
a)1 kmph            b)1.5 kmph              c)2 kmph                 d)2.5 kmph
Answer : A
Explanation :
   Speed downstream = $\frac{Distance}{Time}$ = $\frac{40}{8}$ = 5 kmph
   Speed Upstream =    $ \frac{Distance}{Time}$ = $\frac{1}{2}$ = 3 kmph
   Speed of the stream = $ \frac{(Downstream\:Speed\:- Upstream\:Speed)}{2}$
                              = $\frac{1}{2}$ ( 5-3) = 1 kmph

5.    A boat rows 2 km in 10 minutes along the stream and 12 km in 2 hours against the stream. Find the speed of the stream?
a)    9 kmph           b)3 kmph                c)6 kmph                 d)12 kmph
Answer : B
Explanation:
Let the speed of boat and current be x and y kmph.
 Upstream speed =(x-y) kmph and Downstream speed=(x+y) kmph
Boat rows 2 km in 10 minutes along the stream=>
       Downstream speed= $ \frac{Distance}{Time}$= $ \frac{2}{10/60}$ = 12 kmph
Boat rows 12 km in 2 hours against the stream=>
       Upstream speed= $ \frac{Distance}{Time}$ = $\frac{12}{2}$ = 6 kmph
Downstream speed (x+y)= 12 kmph       
Upstream speed (x-y)= 6 kmph
On solving 1 and 2, we get x=9 kmph and y=3 kmph.
   $\therefore$ speed of the stream = 3 kmph

6.    A man rows 4 km in 30 minutes along the stream and 1 km in 30 minutes against the stream. Find the speed of man in still water?
         a)    3 kmph        b)5 kmph      c)7 kmph       d)8 kmph
Answer: B
Explanation:
Let the speed upstream be x kmph and speed downstream be y kmph.
Man rows 4 km in 30 minutes along the stream=>
     Downstream speed=> (x + y)= $\frac{4}{\frac{30}{60}}$ = $ \frac{4}{\frac{1}{2}}$ = 8 kmph
Man rows  1 km in 30 minutes against the flow =>
      Upstream speed=>(x-y)=$ \frac{1}{\frac{30}{60}}$ =$ \frac{1}{\frac{1}{2}}$ = 2 kmph
Speed of the man in still water= $\frac{(Downstream\:Speed\:+Upstream\:Speed)}{2}$
                                         =$\frac{(8+2)}{2}$ = 5 kmph.

7.    What time will be taken by a boat to travel a distance of 60 km in downstream, if speed of boat in still water is 15 kmph and velocity of current is 5 kmph?
a)1.5 hours                  b)2 hours      c) 2.5 hours             d)3 hours
Answer: D
Explanation :
Given that, Speed of boat in still water = 12 kmph
              Speed of stream (Velocity of current) = 5 kmph
      $\therefore$ Downstream speed of boat = (x + y ) = 15 +5 = 20  kmph
Time taken by boat to travel 60 km in downstream= $\frac{Distance}{Downstream\:Speed}$ = 60/20 = 3 hours

8.    A boat can row 9 kmph in still water. It takes him twice as long as row up as to row down the river. Find the speed of the current?
        a)    2 kmph         b)2.5 kmph        c)3 kmph       d)4 kmph
Answer: C
Explanation :
 Let speed of the boat in still water be x and speed of the current be y.
  Given that Upstream time= 2 x Downstream time
        Downstream speed = 2 x Upstream speed
                     x + y ) = 2 ( x – y )
               => 9 + y = 2 ( 9 – y )
                   => 3y= 9
       Speed of the current = 3 kmph.
       
9.    A man can row 12 kmph in still water and speed of the stream is 6 kmph. It takes 1 hour to row to a place and to come back. How far is the place?
a)4.5 km            b)5 km                    c)5.2 km                 d)5.8 km
Answer : A
Explanation : 
 Let the distance be D.
Speed of the man in still water = 12 kmph
                      Speed of the stream =6 kmph
      Man’s downstream speed (x + y)= 12+6 = 18 kmph
        ;Man’s upstream speed (x - y) = 12-6 = 6 kmph
      Given that time take to cover both the  downstream and upstream is 1 hour.
                          T1  + T2 = 1 hour
  $ \frac{D}{USS}$ + $ \frac{D}{DSS}$ = 1 hour
      $\frac{D}{6}$ + $\frac{D}{18}$ = 1
         $\frac{4D}{18}$ = 1
                    D=$\frac{18}{4}$ = 4.5 km
$\therefore$ the distance = 4.5 km

10.  A boat can row a certain distance downstream in 16 hours and can return the same distance in 24 hours. If the stream flows at the rate of 6 kmph, find the speed of the man in still water?
         a)    36 kmph        b)38 kmph               c)42 kmph               d)50 kmph
Answer : C
Explanation : 
Let the speed of boat in still water = x .    Speed of stream y=8 kmph
         Boat’s downstream speed = (x+6)   Boat’s upstream speed =(x-6)
       Distance = Speed x Time 
 Distance = Upstream speed x 24 hours       Distance = Downstream speed x 16 hours
              = ( x – 6 ) x 24                                     = ( x + 6 ) x 18
                                     24(x-6)= 18(x+6)
              24x - 144 = 18x+ 108
                     6x = 252
                             X = 42  
Speed of boat in still water = 42 kmph

11. Speed of a man in still water is 12 kmph while river is flowing with a speed of 4 kmph and time taken to cover a certain distance upstream is 6 hours more than time taken to cover the same distance downstream. Find the distance?
       a)   90 km             b)96 km                     c)84 km                     d)108 km
Answer : B
Explanation :
Let distance be D .
Given that    speed of man in still water x=12 and speed of stream = 4 kmph
      His upstream speed =(x-y)= 12-4 =8 kmph
           Downstream speed (x+y)= 12+4 = 16 kmph
   Given that  $\frac{D}{USS}$ – $\frac{D}{DSS}$ = 6 hours
ð  $\frac{D}{8}$ – $\frac{D}{16}$ = 6
ð  $\frac{2D - D}{16}$ = 6
ð  D=96 km
$\therefore$ the distance covered is 96 km

12. A steamer goes downstream from one port to another in 4 hours .It covers the same distance upstream in 5 hours. If the speed of the stream is 2  kmph, find the distance between the two ports ?(Staff Selection Commission 2007  SSC Previous Question 2007)
        a)    50 km           b)60 km        c)70 km        d)80 km
Answer : D
Explanation :
     Let the distance between two ports = D
     The downstream speed = $\frac{D}{4}$        Upstream speed = $\frac{D}{5}$
           Given that speed of the stream is 2 kmph
             Speed of the stream = ½(DSS – USS) = 2
                                           = $\frac{1}{2}$ ( $\frac{D}{4}$ – $\frac{D}{5}$)  =2
                                           =>$\frac{5D - 4D}{20}$ = 4
                                           => D = 80
                    $\therefore$ the distance between two ports = 80 km

13. The speed of a motor boat is 30 kmph. It starts from Kakinada port at 8 a.m and reaches Vizag port at 11 a.m . Same day it starts from Vizag port at 12 p.m and reaches Kakinada port at  6 p.m. Find the distance between Kakinada and Vizag and find the speed of the stream?
       a)    80 KM                     b)120km       c)145 km       d)180 km
Answer : B
Explanation :  
Given that boat takes 3 hours to go from Kakinada to Vizag and 6 hours to go from Vizag to Kakinada.
   Let speed of the stream be y
                    Time in Upstream = 2 x Time in downstream
ð  Downstream speed = 2 x Upstream speed
ð       (30 + y)= 2(30-y)
ð  3y =30 => y = 10 kmph
$\therefore$, Speed of the stream = 10 kmph
   Downstream Speed = (x + y) = 30+10 = 40 kmph
    Distance between Vizag and Kakinada = Downstream Speed x Time taken in downstream
                                                           =     40 kmph x 3 hours = 120 km

14. In a river, the ratio of the speeds of the boat in still water and the speed of the stream is 7:3. Again , ratio of the speed of an another boat in still water and speed of the stream is 9:2. What is the ratio of the speeds of the first boat to the second boat in still water?
        a)    7:6               b)7:5            c)6:7             d)8:5
Answer : A
Explanation :
 For the first boat, Speed of the boat in still water : Speed of stream = 7 :3
Then Speed of boat in still water =7x and speed of stream =3x

Similarly, for the second boat, speed of the boat in still water = 9y and speed of the stream = 2 y
     River is same in both conditions, then speed of stream in both cases is equal
ð  3x =2y=> x=$\frac{3}{2}$ y
       Now, the required ratio of speeds of boats = 7x: 9y
ð  7 x $\frac{3y}{2}$ : 9y
ð  21y : 18y
ð  7:6
     The ratio of the speeds of first boat in still water to speed of second boat in still water = 7:6

15. There is a road beside a river. Two men Sudheer and Ravi, started from a place A , moved to another place B and returned to A again. Sudheer started moving on a bike at a speed of 14 kmph, while Ravi sails in boat at speed of 12 kmph. If the speed the river is 3 kmph, which of the two men will return to place A first?
a)Ravi      b)Sudheer     c)Both will reach together    d)Cant be determined
Answer : B
Explanation :
Sudheer travels on bike both ways at a speed of 14 kmph.
Given that speed of Ravi in still water is 12 kmph and speed of the stream is 3 kmph.
Ravi sails his boat in downstream (one way) at (12+3) = 15 kmph and in upstream (another way) at 12-3=9 kmph.
  Average speed of Ravi = $\frac{2ab}{a+b}$ =$\frac{2\times15\times9}{15\dotplus9} $
=270/24 = 10.12 kmph
Clearly Speed of Sudheer is 12 kmph and Speed of Ravi is 10.12 kmph
Clearly Speed of Sudheer > Speed of Ravi.

    $\therefore$ Sudheer reaches the place B first.