646.A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is :
0.5 km/hr
1 km/hr
3.5 km/hr
1.8 km/hr
Explanation:
Suppose he move 4 km downstream in x hours. Then,
Speed downstream =($\dfrac{4}{x}$) km/hr
Speed upstream =( $\dfrac{3}{x}$ ) km/hr
∴ $\dfrac{48}{(4/x)} $+ $\dfrac {48} {(3/x)} $ =14 or x= $\dfrac{1}{2}$
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2(8−6)km/hr=1km/hr
Speed downstream =($\dfrac{4}{x}$) km/hr
Speed upstream =( $\dfrac{3}{x}$ ) km/hr
∴ $\dfrac{48}{(4/x)} $+ $\dfrac {48} {(3/x)} $ =14 or x= $\dfrac{1}{2}$
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2(8−6)km/hr=1km/hr
647.The current of stream runs at the rate of 4 km an hour. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is :
6 km/hr
7.5 km/hr
8 km/hr
6.8 km/hr
Explanation:
Let the speed of boat in still water be x km/hr
$\dfrac{6}{x+4}$+ $\dfrac{6}{x-4} $ = 2
=> $ 6 \left ( \dfrac{x-4+x+4}{(x+4)(x-4)} \right ) $ = 2
=> 6x = $x^{2}-16 $
=>$ x^{2}-6x-16 $ = 0
=>$ x^{2}-8x+2x-16 $= 0
=> x(x-8)+2(x-8) = 0
=> (x+2)(x-8) = 0
=> x = 8km/hr
$\dfrac{6}{x+4}$+ $\dfrac{6}{x-4} $ = 2
=> $ 6 \left ( \dfrac{x-4+x+4}{(x+4)(x-4)} \right ) $ = 2
=> 6x = $x^{2}-16 $
=>$ x^{2}-6x-16 $ = 0
=>$ x^{2}-8x+2x-16 $= 0
=> x(x-8)+2(x-8) = 0
=> (x+2)(x-8) = 0
=> x = 8km/hr
648.The current of a stream runs at 1km/hr. A motor boat goes 35 km. upstream and back again to the starting point in 12 hours. The speed of motor boat in still water is :
6 km/hr
7 km/hr
8.5 km/hr
8 km/hr
Explanation:
Let the speed in still water be x km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12
⇒ 35(2x) = 12(x2 - 1)
⇒ $12x^{2} - 70x - 12$ = 0
⇒ $12x^{2} - 72x + 2x - 12 $ = 0
⇒ 12x(x - 6) + 2 (x - 6) = 0
⇒ (x - 6) (12x + 2) = 0
∴ x = 6 km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12
⇒ 35(2x) = 12(x2 - 1)
⇒ $12x^{2} - 70x - 12$ = 0
⇒ $12x^{2} - 72x + 2x - 12 $ = 0
⇒ 12x(x - 6) + 2 (x - 6) = 0
⇒ (x - 6) (12x + 2) = 0
∴ x = 6 km/hr
649.A girl can row 4 $\dfrac{2}{3} $ km/hr in still water and she finds that it takes her thrice as much time to row up than as to row down the same distance in river. The speed of the current is :
3 $\dfrac{1}{3} $ km/hr
3 $\dfrac{1}{9} $ km/hr
1 $\dfrac{1}{4} $ km/hr
4 $\dfrac{2}{3} $ km/hr
Explanation:
Let speed upstream be x kmph Then speed downstream = 3x kmph
Speed in still water = 1/2(3x+x)kmph=2xkmph
∴2x= 28/3
⇒x=14/3
So Speed upstream =14/3 km/hr
Speed downstream = 14 km/hr
Hence speed of the current = 1/2 (14−14/3)km/hr
= 14/3 km/h
=4 $\dfrac{2}{3} $ km/hr
Speed in still water = 1/2(3x+x)kmph=2xkmph
∴2x= 28/3
⇒x=14/3
So Speed upstream =14/3 km/hr
Speed downstream = 14 km/hr
Hence speed of the current = 1/2 (14−14/3)km/hr
= 14/3 km/h
=4 $\dfrac{2}{3} $ km/hr
674.A person can swim in water at 4 km/h. If the speed of water 2km/h, how many hours will the man take to swim back against the current for 6km?
3 hours
4 hours
5 hours
Insufficient data
Explanation:
Speed Upstream =(4-2) km/hr = 2 km/hr
Time taken to swim 6 km against the surrent is $\dfrac{6}{(4-2)}=3 hours
Time taken to swim 6 km against the surrent is $\dfrac{6}{(4-2)}=3 hours
675.A man can row his boat with the stream at 6km/h and against the stream in 4 km/h. The man’s rate is?
1 kmph
5 kmph
8 kmph
3 kmph
Explanation:
If speed of boat=x
And speed of river=y
Then,
x-y=4 [x=4+y---->{1}]
x+y=6 ---------->{2}
Substituting eqn. 1 in 2
4+y+y=6
2y=6-4
y=2/2
y=1 ------------> {3}
Sub. Eqn. 3 in 1
x=4+y
x=4+1
x=5
Hence, speed of boat is 5 kmph.
And speed of river=y
Then,
x-y=4 [x=4+y---->{1}]
x+y=6 ---------->{2}
Substituting eqn. 1 in 2
4+y+y=6
2y=6-4
y=2/2
y=1 ------------> {3}
Sub. Eqn. 3 in 1
x=4+y
x=4+1
x=5
Hence, speed of boat is 5 kmph.
677.A person can row at 9kmph and still water. He takes 4 ½ 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?
32 km
25 km
28 m
None of these
Explanation:
Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
1278.A person can row 750 metres against the stream in 11 ¼ minutes and returns in 7 ½ minutes. The speed of the person in in still water is :
60
None of these
2 km/hr
3 km/hr
Explanation:
The speed in upstream = .75 * (4/45 )*60 = 4 kmph
The speed in downstream = .75 *(2/15) *60 = 6 kmph
Speed in still water =1/2(4+6) = 5 kmph
The speed in downstream = .75 *(2/15) *60 = 6 kmph
Speed in still water =1/2(4+6) = 5 kmph
1279.If a man rows at the rate of 6 kmph in still water and his rate aginst the current is 4.5 kmph, then the mans rate along the current is
4km/hr
5 km/hr
6 kmph
7.5 kmph
Explanation:
still water speed 6 kmph.
upstream 4.5 kmph.
speed decreased due to the water current 6-4.5 =1.5kmph which is the speed of the stream
while rowing downstream this speed will add up to the rowing speed in still water
so the speed downstream i.e along the current is 6+1.5 =7.5 kmph
upstream 4.5 kmph.
speed decreased due to the water current 6-4.5 =1.5kmph which is the speed of the stream
while rowing downstream this speed will add up to the rowing speed in still water
so the speed downstream i.e along the current is 6+1.5 =7.5 kmph
1280.A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes. The speed of the current is :
6.5kmph
8 kmph
1 kmph
2 kmph
Explanation:
Speed upstream = 1 km in 20 minutes.
So the upstream speed in km per hour = (1 / 20) * 60 = 3 km/hr
Speed downstream = 1 km in 12 m
So the downstream speed in km per hour = (1 / 12 )* 60 = 5 km/hr
Therefore speed of the current = (5 - 3)/2 km/hr = 1 km/hr
So the upstream speed in km per hour = (1 / 20) * 60 = 3 km/hr
Speed downstream = 1 km in 12 m
So the downstream speed in km per hour = (1 / 12 )* 60 = 5 km/hr
Therefore speed of the current = (5 - 3)/2 km/hr = 1 km/hr
1281.A man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph. What is the time taken to row a distance of 90 km down the stream ?
3 kmph
2.5 kmph
8hrs
5 hrs
1282.If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream
15 hrs
20 hrs
1kmph
2kmph
1400.A man rows to a place 48km distant and back in 14 hours. He finds
that he can row 4km with the stream in the same time as 3km against the
stream. The rate of the stream is
that he can row 4km with the stream in the same time as 3km against the
stream. The rate of the stream is
1.1 km/hr
1.2 km/hr
2.2km/hr
1.7 km/hr
Explanation:
Suppose he moves 4km downstream in x hours
Then, downstream a= 4 / x km/hr
Speed upstream b = 3/ x km/hr
48 / 4 /x + 48 / 3/x = 14
x/4 + x/3 = 14/48 = ¼
3x + 4x / 12 = ¼ è 7x x 4 = 12 è x = 3/7
a=28/3 km/hr b = 7km/hr
rate of stream = ½ (28/3 – 7 )
= 7/6 = 1.1 km/hr
Suppose he moves 4km downstream in x hours
Then, downstream a= 4 / x km/hr
Speed upstream b = 3/ x km/hr
48 / 4 /x + 48 / 3/x = 14
x/4 + x/3 = 14/48 = ¼
3x + 4x / 12 = ¼ è 7x x 4 = 12 è x = 3/7
a=28/3 km/hr b = 7km/hr
rate of stream = ½ (28/3 – 7 )
= 7/6 = 1.1 km/hr
1401.The current of stream runs at 1kmph. A motor baot goes 35km
upstream and back again to the starting point in 12hours. The speed of the
motor boat in still water is
upstream and back again to the starting point in 12hours. The speed of the
motor boat in still water is
8km/hr
3km/hr
6km/hr
5km/hr
Explanation:
Let the speed of the motor boat in still water be x kmph then.
Speed downstream = x+1 km/hr
Speed upstream = x-1 km/hr
35/x+1 + 35/x-1 = 12
x-1+x+1/ (x+1) (x-1) = 12/35 == > 2x / x2 – 1 = 12/35
= 6x2 – 35 x – 6 = 0
= 6x2 – 36 x+x – 6 = 0
= 6x (x-6) + 1 (x-6) = 0 è (6x+1) (x-6) = 0
x=6 km/hr
Let the speed of the motor boat in still water be x kmph then.
Speed downstream = x+1 km/hr
Speed upstream = x-1 km/hr
35/x+1 + 35/x-1 = 12
x-1+x+1/ (x+1) (x-1) = 12/35 == > 2x / x2 – 1 = 12/35
= 6x2 – 35 x – 6 = 0
= 6x2 – 36 x+x – 6 = 0
= 6x (x-6) + 1 (x-6) = 0 è (6x+1) (x-6) = 0
x=6 km/hr
1402.A boat covers 24km upstream and 36km downstream in 6 hours while
it cover 35km upstream and 24km downstream in 6 ½ hours. The velocity of
the current is
it cover 35km upstream and 24km downstream in 6 ½ hours. The velocity of
the current is
3km/hr
2km/hr
1km/hr
4km/hr
Explanation:
Let the rate upstream = x km / hr and
Rate downstream = y km/hr
24/x + 36/y = 6 è 36 x + 24y = 6 xy à 1
36/x + 24/y = 6 ½ à 24x + 36y = 13/2 xy à 2
letting 1/x = a, 1/y = B
1+2 è 60 (1/x + 1/y) = 25/2 è 1/x +1/y = 5/24à 3
2-1 à 12 (1/x – 1/y) = ½ è 1/x – 1/y = 1/24 à 4
3+4 è x = 8 solving we get y=12
speed of stream = ½ (12-8) = 2km/hr
Let the rate upstream = x km / hr and
Rate downstream = y km/hr
24/x + 36/y = 6 è 36 x + 24y = 6 xy à 1
36/x + 24/y = 6 ½ à 24x + 36y = 13/2 xy à 2
letting 1/x = a, 1/y = B
1+2 è 60 (1/x + 1/y) = 25/2 è 1/x +1/y = 5/24à 3
2-1 à 12 (1/x – 1/y) = ½ è 1/x – 1/y = 1/24 à 4
3+4 è x = 8 solving we get y=12
speed of stream = ½ (12-8) = 2km/hr
1403.The speed of a boat in still water is 15km/hr and the rate of current is
3 km/hr. the distance traveled downstream in 12 minutes is
3 km/hr. the distance traveled downstream in 12 minutes is
3.0 km
4.6 km
3.6 km
6.9 km
Explanation:
Speed in still water = 15km/hr
½ (a+b) = 15km/hr
a+b = 30 km/hr -- (1)
speed of current = 3 km/hr
½ (a-b) = 3km/hr
a-b= 6 km/hr –(2)
1+2 è 2a = 36 è a=18 km/hr
ie., speed downstream = 18 km/hr
distance traveled downstream = 18 x 12/60 km = 3.6 km
Speed in still water = 15km/hr
½ (a+b) = 15km/hr
a+b = 30 km/hr -- (1)
speed of current = 3 km/hr
½ (a-b) = 3km/hr
a-b= 6 km/hr –(2)
1+2 è 2a = 36 è a=18 km/hr
ie., speed downstream = 18 km/hr
distance traveled downstream = 18 x 12/60 km = 3.6 km
1404.A man can row 5kmph in still water. If the river is running at 1kmph,
it makes him 75minutes to row to a place and back. How far is the place?
it makes him 75minutes to row to a place and back. How far is the place?
3 km
4 km
5 km
None of these
Explanation:
Speed in still water , ½ (a+b) = 5 == > a+b = 10 -- (1)
Speed of the stream , ½ (a-b) = 1 è a-b = 2 --(2)
Solving 1 and 2 gives a=6 ; b=4
Let the required distance be x km
x/6 + x / 4 = 75/60 == > 10x/24 = 75/60
x = 24x 75/10x60 = 3
required distance = 3 km
Speed in still water , ½ (a+b) = 5 == > a+b = 10 -- (1)
Speed of the stream , ½ (a-b) = 1 è a-b = 2 --(2)
Solving 1 and 2 gives a=6 ; b=4
Let the required distance be x km
x/6 + x / 4 = 75/60 == > 10x/24 = 75/60
x = 24x 75/10x60 = 3
required distance = 3 km
1405.If a man rows at the rate of 5kmph in still water and his rate against
the current is 3.5kmph then the mans rate along the current is
the current is 3.5kmph then the mans rate along the current is
8km/hr
3km/hr
6.5km/hr
None of these
Explanation:
Speed in still water = ½ (a+b) km/hr
Answer with Explanation:
Speed in still water , ½ (a+b) = 5km/hr è a+b =10
Speed upstream b = 3.5 km/hr
Speed along the current i.e, downstream a = 10-3.5 = 6.5km/hr
Speed in still water = ½ (a+b) km/hr
Answer with Explanation:
Speed in still water , ½ (a+b) = 5km/hr è a+b =10
Speed upstream b = 3.5 km/hr
Speed along the current i.e, downstream a = 10-3.5 = 6.5km/hr
1406.There is road besides a river. Two friends started from a place A, moved to a temple
situated at another place B and then returned to A again. One of them moves on a cycle at
a speed of 12 km/hr, while the other 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?
situated at another place B and then returned to A again. One of them moves on a cycle at
a speed of 12 km/hr, while the other 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?
Both
Boater
Cyclist
None of these
Explanation:
The cyclist moves both ways at a speed of 12khr so average speed fo the cyclist – 12 km/hr
Also bat sailor moves downstream at 10+4 = 14km/hr and upstream 10- 4 = 6km/hr
Average speed of the boat sailor = 2 x 14 x 6 / 14 +6 = 42/ 5 = 8.4km/hr
The average speed of cyclist is greater cyclist comes first and return to place A
The cyclist moves both ways at a speed of 12khr so average speed fo the cyclist – 12 km/hr
Also bat sailor moves downstream at 10+4 = 14km/hr and upstream 10- 4 = 6km/hr
Average speed of the boat sailor = 2 x 14 x 6 / 14 +6 = 42/ 5 = 8.4km/hr
The average speed of cyclist is greater cyclist comes first and return to place A
2436.A boat moves downstream at the rate of one km in 5 minutes and upstream at the rate of 4 km an hour. What is the velocity of the current?
4 km/hr
2 km/hr
3 km/hr
1 km/hr
Explanation:
Speed downstream = $\dfrac{1}{\left(\dfrac{5}{60}\right)} = 12\text{ km/hr}$
Speed upstream $=\dfrac{4}{1}\text{ = 4 km/hr}$
velocity of the current $=\dfrac{1}{2}(12-4)= \text{4 km/hr}$