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# Aptitude::Boats and Streams

Home > Quantitative Aptitude > Boats and Streams > Subjective Solved Examples

Example 1 / 16

A man's speed with the current is 20 km/hr and the speed of the current is 3 km/hr. The man's speed against the current is
Man's speed with the current = 20 km/hr
speed of the man + speed of the current = 20 km/hr
speed of the current is 3 km/hr
Hence, speed of the man = 20-3 = 17 km/hr
man's speed against the current = speed of the man - speed of the current
= 17-3 = 14 km/hr Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where,
u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
we have to first take out the speed of man. Then, put the formula and take out man’s speed against the current. Example 2 / 16

A man takes twice as long to row a distance against the stream as to row the same distance in favor of the stream. The ratio of the speed of the boat (in still water) and the stream is
Let speed upstream = x
Then, speed downstream = 2x
Speed in still water =$$\frac{2x+x}{2}$$=$$\frac{3x}{2}$$
Speed of the stream =$$\frac{2x−x}{2}$$=$$\frac{x}{2}$$
Speed in still water : Speed of the stream =$$\frac{3x}{2}$$:$$\frac{x}{2}$$=3:1 Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
using the formulae, take out the speeds and find the ratio. Example 3 / 16

If a man rows at the rate of 5 kmph in still water and his rate against the current is 3 kmph, then the man's rate along the current is
Let the rate along with the current is x km/hr

$$\frac{x+3}{2}$$=5
⇒x+3=10 ⇒x=7 kmph Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where,
u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
based on the formula. Example 4 / 16

A man can row 6 kmph is still water. If the river is running at 4 kmph it takes 120 min to row to a place and back. How far is the place?
Speed in still water = 6 kmph
Speed of the stream = 4 kmph
Speed upstream = (6-4)= 2 kmph
Speed downstream = (6+4)= 10 kmph
Total time = 90 minutes = $$\frac{120}{60}$$ hour = 2 hour
Let L be the distance. Then
$$\frac{L}{10}$$+$$\frac{L}{2}$$=2
$$\frac{12L}{20}$$=2
L= 3.33 km Ans.

Distance= speed*time
1.Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
take out the speeds and time and put in the formula, distance = speed*time and find the distance. Example 5 / 16

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?
Let the speed of Rahul in still water be x mph
and the speed of the current be y mph
Then, Speed upstream =(x−y)=(x−y) mph
Speed downstream =(x+y)=(x+y) mph

Distance = 12 miles

Time taken to travel upstream - Time taken to travel downstream = 6 hours
⇒$$\frac{12}{x−y}$$−$$\frac{12}{x+y}$$=6
⇒12(x+y)−12(x−y)=6($${x}^{2}$$−$${y}^{2}$$)
⇒24y=6($${x}^{2}$$−$${y}^{2}$$)
⇒4y=($${x}^{2}$$−$${y}^{2}$$)
⇒$${x}^{2}$$=($${y}^{2}$$+4y)-----(i)
Now he doubles his speed. i.e., his new speed =2x
Now, Speed upstream =(2x−y) mph
Speed downstream =(2x+y) mph
In this case, Time taken to travel upstream - Time taken to travel downstream = 1 hour
⇒$$\frac{12}{2x−y}$$−$$\frac{12}{2x+y}$$=1
⇒12(2x+y)−12(2x−y)=4($${x}^{2}$$−$${y}^{2}$$)
⇒24y=4($${x}^{2}$$−$${y}^{2}$$)
⇒4$${x}^{2}$$=$${y}^{2}$$+24y----- (ii)

(Equation i× iv)=> 4$${x}^{2}$$=4($${y}^{2}$$+4y)⋯(iii)

From Equation ii and iii, we have,
$${y}^{2}$$+24y=4($${y}^{2}$$+4y)
⇒$${y}^{2}$$+24y=4$${y}^{2}$$+16y
⇒3$${y}^{2}$$=8y
⇒3y=8
⇒y=$$\frac{8}{3}$$ mph

i.e., speed of the current =$$\frac{8}{3}$$ mph=2$$\frac{2}{3}$$ mph
Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
based on the formula. Double the rate and find the speed. Example 6 / 16

A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current
Speed upstream = $$\frac{3}{\frac{20}{60}}$$ = 9 km/hr
Speed downstream = $$\frac{3}{\frac{18}{60}}$$ = 10 km/hr

Rate of current =$$\frac{10−9}{2}$$=12 km/hr Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream

NA
based on formula to find the rate of current. Example 7 / 16

A boat takes 40 hours for traveling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 8 kmph and the speed of the boat in still water is 16 kmph, what is the distance between A and B?
The velocity of the stream = 8 kmph
Speed of the boat in still water is 16 kmph

Speed downstream = (16+8) = 24 kmph
Speed upstream = (16-8) = 8 kmph

Let the distance between A and B be x km

Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B) = 40 hours
⇒$$\frac{x}{24}$$+$$\frac{\frac{x}{2}}{8}$$=40
⇒$$\frac{x}{24}$$+$$\frac{x}{16}$$=40
⇒$$\frac{40x}{224}$$=40
X=224 km

i.e., distance between A and B = 224km Ans.

distance = speed*time
1. Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
take out the speeds and time and put in the formula, distance = speed*time and find the distance. Example 8 / 16

If a man's rate with the current is 15 km/hr and the rate of the current is 11⁄2 km/hr, then his rate against the current is
Speed downstream = 15 km/hr
Rate of the current= 1$$\frac{1}{2}$$ km/hr

Speed in still water = 15 - 1$$\frac{1}{2}$$ = 13$$\frac{1}{2}$$km/hr

Rate against the current = 13$$\frac{1}{2}$$ km/hr - 1$$\frac{1}{2}$$= 12 km/hr Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
directly based on the formula of speed in still water and rate of the current. Example 9 / 16

The speed of the boat in still water in 6 kmph. It can travel downstream through 21 kms in 3 hrs. In what time would it cover the same distance upstream?
Speed of the boat in still water = 6 km/hr

Speed downstream =$$\frac{21}{3}$$ = 7 km/hr

Speed of the stream = 7-6 = 1 km/hr

Speed upstream = 6-1 = 5 km/hr
Time taken to cover 21 km upstream =$$\frac{21}{5}$$= 4.2 hours Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
find the speed, distance is given, take out the time as distance=speed * time. Example 10 / 16

The current of a stream runs at the rate of 2 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motor boat in still water?
Let the speed of the boat in still water =x km/hr
Speed of the current = 2 km/hr

Then, speed downstream =(x+2) km/hr
speed upstream =(x−2) km/hr

Total time taken to travel 10 km upstream and back = 55 minutes =$$\frac{55}{60}$$ hour =$$\frac{11}{12}$$ hour
⇒$$\frac{10}{x−2}$$+$$\frac{10}{x+2}$$=$$\frac{11}{12}$$
=> 120(x+2)+120(x−2)=11($${x}^{2}$$−4)
240x=11$${x}^{2}$$−44
11$${x}^{2}$$−240x−44=0
11$${x}^{2}$$−242x+2x−44=0
11x(x−22)+2(x−22)=0
(x−22)(11x+2)=0 x=22 or $$\frac{−2}{11}$$
Since x cannot be negative, x = 22

i.e., speed of the boat in still water = 22 km/hr Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
take out the speeds, then by using formula time=$$\frac{distance}{speed}$$, add both the time and find x. Example 11 / 16

The speed of a boat in still water is 10 kmph. If it can travel 2 km upstream in 1 hr, what time it would take to travel the same distance downstream?
Speed of the boat in still water = 10 km/hr

Speed upstream = $$\frac{2}{1}$$= 2 km/hr

Speed of the stream = 10-2 = 8 km/hr

Speed downstream = (10+2) = 12 km/hr

Time taken to travel 2 km downstream =$$\frac{2}{12}$$ hr = $$\frac{2×60}{12}$$
= 10 minutes Ans.

distance=speed*time
1.Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
find the speed, distance is given, use the formula, distance=speed*time. Example 12 / 16

If a man's rate with the current is 12 km/hr and the rate of the current is 1$$\frac{1}{2}$$ km/hr, then his rate against the current is
Speed downstream = 12 km/hr
Rate of the current= 1$$\frac{1}{2}$$ km/hr

Speed in still water = 12 - 1$$\frac{1}{2}$$= 10$$\frac{1}{2}$$km/hr

Rate against the current = 10$$\frac{1}{2}$$ km/hr - 1$$\frac{1}{2}$$
= 9 km/hr Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
based on direct formula of boats and streams. Example 13 / 16

A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Speed in still water= 15 kmph
Speed of stream= 5 kmph
Speed of downstream= speed in still water+ speed of a stream
= 15+5= 20 kmph. Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
based on direct formula of boats and streams. Example 14 / 16

The speed at which a man can row a boat in still water is 24 kmph. If he rows downstream, where the speed of current is 12 kmph, what time will he take to cover 60 metres?
Speed of the boat downstream = 24+12= 24 kmph
= 36 * 5/18 = 10 m/s
Hence time taken to cover 60 m = 60/10 = 6 seconds. Ans.

distance=speed*time.
1.Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
find the speed, distance is given, use the formula, distance=speed*time. Example 15 / 16

A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Let the distance between A and B be x km.
Total time = $$\frac{x}{(9 + 1)$$ +$$\frac{x}{(9 - 1)}$$ = 4.5
=> $$\frac{x}{10}$$ + $$\frac{x}{8}$$ = $$\frac{9}{2}$$
=>$$\frac{(4x + 5x)}{40}$$ = $$\frac{9}{2}$$
=> x = 20 km. Ans.

distance=speed*time
1.Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
take the distance as x. find the speed and add up in terms of time and use the formula, time=$$\frac{distance}{speed}$$ Example 16 / 16

A man can row 9 1/3 km/hr in still water and he finds that is thrice as much time to row up than as to row down the same distance in river. The speed of the current is:
Let Speed upstream = x km/hr

Speed downstream = 3x km/hr

Speed in still water = $$\frac{1}{2}$$(x+3x) km/hr = 2x km/hr

Speed of current = $$\frac{1}{2}$$ (3x-x) km/hr = x km/hr

2x = $$\frac{28}{3}$$ or x = $$\frac{14}{3}$$ = 4$$\frac{2}{3}$$ km/hr. Ans.

Speed downstream = (u + v) km/hr.
2. Speed upstream = (u - v) km/hr.
3. Speed in still water = 1(a + b)/2 km/hr.
4. Rate of stream = 1(a - b)/2 km/hr.
Where, u= speed in still water
v = Rate of stream
a = speed of downstream
b= speed of upstream
NA
based on direct formula of boats and streams. 