Quant Notes | Boat and Stream
Downstream: when the boat (or swimmer) moves in the same direction as that of the stream.
1. Speed of boat = x km/hr
2. Speed of current =y km/hr
3.Speed of the boat downstream = x+y km/hr
4. Speed of the boat upstream = x−y km/hr
5. Speed of boat in still water = 1/2(downstream + upstream)
6. Speed of current= 1/2(downstream − upstream)
The application of example as below as-
Q1. A boat can travel with a speed of 13 km/hr. in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream. a. 3.5hr
b. 4hr
c. 5hr
d. 4.5hr
e. None of these
Solution :
Speed=distance /time
Downstream speed=d/t
Downstream =x+y
x+y=d/t
x+y=17
17=68/t
t=4hr
Q2. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
a. 3.5hr
b. 4hr
c. 5hr
d. 4.5hr
e. None of these
Solution :
Speed downstreams=(15 + 3)km/hr = 18 km/hrs.
Distance travelled= (18 x 12/60)km = 3.6km
Q3. 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 stream is
a. 3:1
b. 2:4
c. 3 km/hr
d. 4 km/hr
e. None of these
Solution :
Let speed downstream = x km/hr
Then Speed upstream = 2x km/hr
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
Q4. A boat has to travel upstream 20 km distance from point X of a river to point Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 min 40 s. What is the speed of the boat?
a. 66 kmph
b. 72 kmph
c. 48 kmph
d. Cannot be determined
e. 75 kmph
Solution :Let speed of boat in still water=x kmph
speed of stream=y kmph
20/x-y + 2/x-y=25/36
Here we cannot find the required answer as
there are two variable in one equation .
Q5. A swimmer can swim 33⅓% faster in downstream than in upstream. He takes 4 hours to swim a distance of 32 km in still water. Speed of stream is how much percent of upstream speed?
a. 16.33%
b. 12.25%
c. 16.67%
d. 14.28%
e. none of these.
Solution :
Let speed of boat in upstream= 3xkmph
speed of Boat in downstream=4*3x/3=4kmph
speed of stream=4x-3x/2=0.5x
Required percentage=0.5x*100/3x=16.67%
