## Quant Quiz On Boat & Streams Day 21 Bag

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• Ram goes downstream with a boat to some destination and returns upstream to his original places in 6 hours. If the speed of the boat in still water and the stream are 12km/hr and 5 km/hr respectively, then find the distance of the destination form the starting position.
A) 25km
B) 26.67km
C) 33km
D) 29.75km
E) 20km

Option D
Solution:
T = 2xD/(x^2 – y^2)
=> D = 119*6/2*12 = 29.75km
• A boat travels downstream for 14km and upstream for 9km. If the boat took total of  5 hours for its journey. What is the speed of the river flow if the speed of the boat in still water is 5km/hr?
A) 8km/hr.
B) 2km/hr.
C) 6km/hr.
D) 5km/hr.
E) 3km/hr.

Option B
Solution:
Let the speed of the stream be x km/hr.
Upward  speed = (5 – x)km/hr.
Downward speed = (5 + x)km/hr.
14/(5+x) + 9/(5-x) = 5
=> x = 2km/hr.
• When a person is moving in the direction perpendicular to the direction of the current is 20km/hr , speed of the current is 5km/hr. Then find the speed of the person against the current?
A) 10km/hr.
B) 15km/hr.
C) 30km/hr.
D) 25km/hr.
E) 11km/hr.

Option A
Solution:
Speed of the person = 20 – 5 = 15km/hr
Speed of the person against the current = 15 – 5 = 10km/hr.
• A boat goes 6 km an hour in still water, it takes thrice as much time in going the same distance against the current comparison to the direction of the current. Find the speed of the current.
A) 5km/hr
B) 3km/hr
C) 8km/hr
D) 9km/hr
E) 12km/hr

Option B
Solution:
Let the speed of the stream be x km/hr
speed of the still water = 6 km/hr
Downstream speed = (6+x) km/hr
Upstream speed = (6-x)km/hr
Now,
3[D/(6+x)] = D/(6-x)
=> x = 3 km/hr
• There are two places A and B which are separated by a distance of 100k. Two boats starts form both the places at the same time towards each other. If one boat is going downstream then the other one is going upstream, if the speed of A and B is 12km/hr. and 13km/hr. respectively. Find at how much time will they meet each other.
A) 10hrs.
B) 4 hrs.
C) 8hrs.
D) 6hrs.
E) 7hrs.

Option B
Solution:
Downstream = (12+x)km/hr
Upstream = (13-x)km/hr
Time = Distance / Relative speed
Relative speed = 12 + x + 13 – x  = 25 km/hr
Time = 100/25 = 4 hours
• A girl was travelling in a boat, suddenly wind starts blowing and blows her hat and started floating back downstream. The boat continued to travel upstream for 12 more minutes before she realized that her hat had fallen off. She turned back downstream and she caught her hat as soon as she reached the starting point. If her hat flew off exactly 2km from where she started. What is the speed of the water?
A) 12km/hr
B) 8km/hr
C) 5km/hr
D) 9km/hr
E) 10km/hr

Option C
Solution:
Distance = 2 km
Time = 2 * 12 (doubles ) = 24 mins. = 2/5 hr.
Speed = 2 / (2/5) = 5 km/hr.
• A ship sails 30km of a river towards  upstream in 6 hours. How long will it take to cover the same distance downstream. If the speed of the current is (1/4)rd of the speed of the boat in still water.
A) 2 hrs
B) 4.5hrs
C) 5 hrs
D) 3.6hrs
E) 5.5 hrs

Option D
Solution:
Let x be speed of the boat and y be the speed of the current.
Downstream speed =  x + y
Upstream speed = x – y
x –y = 30/6  = 5 km/hr.
Now,
x = 4y
x – y = 4y – y = 3y
=> x = (20/3)km/hr and  y = (5/3)km/hr
Therefore, x + y = (25/3) km/hr.
Time during downstream = 90/25 =3.6 hrs.
• A man can row 6km/hr in still water. If the speed of the current is 2km/hr, it takes 4 hours more in upstream than in the downstream for the same distance. Find the distance.
A) 44km
B) 40km
C) 32km
D) 50km
E) 45km

Option C
Solution:
Let the distance be D.
Downstream speed =  8 km/hr
Upstream speed = 4km/hr
From the question,
Upstream = Downstream + 4
D/4 = D/8 + 4
D/4 = (D + 32)/8
D = 32 km
• The speed of the motor boat is that of the current of water is 36:5 . The boat goes along with the current in 5 hours 10 minutes . How much time it will take to come back .
A) 45/2
B) 41/6
C) 55/3
D) 38/7
E) 52/8

Option B
Solution:
S1/S2 = T1/T2
(36 + 5)/(36 – 5) = x/(31/6)
=> x = 41/6 = 6 hours 50 minutes
• In a fixed time, a boy swims double the distance along the current that he swims against the current. If the speed of the current is 3km/hr. , then what is the  speed of the boy in still water ?
A) 9 km/hr
B) 13km/hr
C) 15km/hr
D) 22km/hr
E) 10km/hr

Option A
Solution:
Let the speed of boy in still water be x km/hr
and the speed of current is given = 3 km/hr
Downstream speed = (x+3) km/hr
Upstream speed = (x-3) km/hr
Let time be t hours
(x+3)*t = 2 {(x-3)*t}
=> x = 9 km/hr

• A boat can cover 25 km upstream and 42 km downstream together in 7 hours. Also it can cover 30 km upstream and 63 km downstream together in 9 hours. What is the speed of the boat in still water?
A) 13 km/hr
B) 8 km/hr
C) 7 km/hr
D) 11 km/hr
E) 16 km/hr

Option A
Solution:

Upstream speed in both cases is 25 and 30 resp. Ratio is 25 : 30 = 5 : 6. So let times in both cases be 5x and 6x
Downstream speed in both cases is 42 and 63 resp. Ratio is 42 : 63 = 2 : 3. So let times in both cases be 2y and 3y
So 5x + 2y = 7
and 6x + 3y = 9
Solve both, x = 1, y = 1
So upstream speed is = 25/5x = 5 km/hr
And downstream = 42/2y = 21 km/hr
So speed of boat is 1/2 * (5+21)
• A man rows to a certain place and comes back, but by mistake he covers 1/3rd more distance while coming back. The total time for this journey is 10 hours. The ratio of speed of boat to that of stream is 2 : 1. If the difference between upstream and downstream speed is 12km/hr, then how much time will the man take to reach to starting point from his present position?
A) 35 minutes
B) 45 minutes
C) 60 minutes
D) 40 minutes
E) 55 minutes

Option D
Solution:

Speed of boat and stream – 2x and x respectively. So downstream speed = 2x+x = 3x, and upstream speed = 2x-x = x
Let total distance between points is d km
So he covered d km downstream, and while coming back i.e. upstream he covers d + 1/3 *d = 4d/3 km
Total time for this journey is 10 hrs. So
d/3x + (4d/3)/x = 10
Solve, d = 6x
Now also given, that (2x+x) – (2x-x) = 12
Solve, x = 6
So d = 36 km
So to come to original point, he will have to cover 1/3 * 36 = 12 km
And with speed 3x = 18 km/hr(downstream)
So time is 12/18 * 60 = 40 minutes
• A man can row at a speed of 15 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 9 km/hr. Find his average speed for total journey.
A) 10.4 km/hr
B) 8.4 km/hr
C) 9.1 km/hr
D) 5.2 km/hr
E) 9.6 km/hr

Option E
Solution:

When the distance is same, then average speed throughout journey would be:
Speed downstream * Speed upstream/speed in still water.
So here average speed = (15+9)*(15-9)/15 = 9.6 km/hr
• A boat takes 5 hours for travelling downstream from point A to point B and coming back to point C at 3/4th of total distance between A and B from point B. If the velocity of the stream is 3 kmph and the speed of the boat in still water is 9 kmph, what is the distance between A and B?
A) 24 km
B) 32 km
C) 27 km
D) 21 km
E) 34 km

Option A
Solution:

Let total distance from A to B= d km, So CB = 3d/4 km
So
d/(9+3) + (3d/4)/(9-3) = 5
Solve, d = 24 km
• At its usual rowing rate, a boat can travel 18 km downstream in 4 hours less than it takes to travel the same distance upstream. But if he the usual rowing rate for his 28-km round trip was 2/3rd, the downstream 14 km would then take 12 hours less than the upstream 14 km. What is the speed of the current?
A) 1.5 km/h
B) 3 km/h
C) 2 km/h
D) 3.5 km/h
E) 4 km/hr

Option B
Solution:

Let speed of boat = x km/hr, and of current = y km/hr
So
18/(x-y) = 18/(x+y) + 4
Gives x2 = 9y + y2……..(1)
Now when speed of boat is 2x/3
14/(2x/3 -y) = 14/(2x/3 +y) + 12
42/(2x-3y) = 42/(2x+3y) + 12
Gives 4x2 = 21y + 9y2…………(2)
From (1), put value of x2 in (2) and solve
Solving, x = 6, y = 3
• A boat can row to a place 120 km away and come back in 25 hours. The time to row 24 km with the stream is same as the time to row 16 km against the stream. Find the speed of current.
A) 1.5 km/h
B) 3 km/h
C) 2 km/h
D) 3.5 km/h
E) 4 km/hr

Option C
Solution:

Downstream speed = 24/x km/hr
Upstream speed = 16/x km/hr
120/(24/x) + 120/(16/x) = 25
Solve, x = 2 km/hr
So, downstream speed = 12 km/hr, upstream speed = 8 km/hr
Speed of current = 1/2 * (12 – 8) km/hr
• A boatman can row 4 Km against the stream in 20 minutes and return in 24 minutes. Find the speed of boatman in still water.
A) 10 km/hr
B) 8 km/hr
C) 15 km/hr
D) 12 km/hr
E) 11 km/hr

Option E
Solution:

Upstream speed = 4/20 * 60 = 12 km/hr
Downstream speed = 4/24 * 60 = 10 km/hr
Speed of boatman = 1/2 (12+10) = 11 km/hr
• A man can row a certain distance downstream in 3 hours and return the same distance in 9 hours. If the speed of current is 18 km/hr, find the speed of man in still water.
A) 47 km/hr
B) 48 km/hr
C) 42 km/hr
D) 50 km/hr
E) 36 km/hr

Option E
Solution:

Use formula:
B = [tu + td] / [tu – td] * R
B = [9+3] / [9-3] * 18
B = 36 km/hr
• Four times the downstream speed is 8 more than 15 times the upstream speed. If difference between downstream and upstream speed is 24 km/hr, then what is the ratio of speed in still water to the speed of the current?
A) 9 : 2
B) 5 : 3
C) 7 : 1
D) 4 : 1
E) 7 : 3

Option B
Solution:

Let speed in still water = x km/hr, of current = y km/hr
So
4 (x+y) = 15(x-y) + 8
Solve, 11x – 19y + 8 = 0…….(1)
Also (x+y) – (x-y) = 24
So y = 12
Put in (1). x = 20
So x/y = 20/12 = 5/3
• A boat can cover 14 km upstream and 21 km downstream together in 3 hours. Also it can cover 21 km upstream and 42 km downstream together in 5 hours. What is the speed of current?
A) 13 km/hr
B) 8 km/hr
C) 7 km/hr
D) 11 km/hr
E) 16 km/hr

Option C
Solution:

Upstream speed in both cases is 14 and 21 resp. Ratio is 14 : 21 = 2 : 3. So let times in both cases be 2x and 3x
Downstream speed in both cases is 21 and 42 resp. Ratio is 21 : 42 = 1 : 2. So let times in both cases be y and 2y
So 2x + y = 3
and 3x + 2y = 5
Solve both, x = 1, y = 1
So upstream speed is = 14/2x = 7 km/hr
And downstream = 21/y = 21 km/hr
So speed of current is 1/2 * (21-7)
1. A boat can cover 21 km in the direction of current and 15 km against the current in 3 hours each. Find the speed of current.
A) 4.5 km/hr
B) 2.5 km/hr
C) 3 km/hr
D) 1 km/hr
E) 6 km/hr

Option D
Solution:

Downstream speed = 21/3 = 7 km/hr
Upstream speed = 15/3 = 5 km/hr
So speed of current = 1/2 * (7-5)
2. A boat whose speed is 6 km/hr can travel 7 km upstream and back in 4 hours. What is the speed of the boat in still water?
A) 10 km/hr
B) 8 km/hr
C) 11 km/hr
D) 12 km/hr
E) 15 km/hr

Option B
Solution:

Let speed of boat is x km/hr
So
7/(x+6) + 7/(x-6) = 4
Solve, x = 8 km/hr [ignore the negative root because speed cannot be negative]
3. A boat can cover 40 km upstream and 60 km downstream together in 13 hours. Also it can cover 50 km upstream and 72 km downstream together in 16 hours. What is the speed of the boat in still water?
A) 5.5 km/hr
B) 6.5 km/hr
C) 8.5 km/hr
D) 3.5 km/hr
E) None of these

Option C
Solution:

Upstream speed in both cases is 40 and 50. Ratio is 40 : 50 = 4 : 5. So let times in both cases be 4x and 5x
Downstream speed in both cases is 60 and 72 resp. Ratio is 60 : 72 = 5 : 6. So let times in both cases be 5y and 6y
So 4x + 5y = 13
and 5x + 6y = 16
Solve both, x = 2, y = 1
So upstream speed is = 40/4x = 5 km/hr
And downstream = 60/5y = 12 km/hr
So speed of boat is 1/2 * (5+12)
4. A boat can row to a place 56 km away and come back in 22 hours. The time to row 21 km with the stream is same as the time to row 12 km against the stream. Find the speed of boat in still water.
A) 1.5 kmph
B) 3.5 kmph
C) 5.5 kmph
D) 7.5 kmph
E) None of these

Option C
Solution:

Downstream speed = 21/x km/hr
Upstream speed = 12/x km/hr
56/(21/x) + 56/(12/x) = 22
Solve, x = 3 km/hr
So, downstream speed = 7 km/hr, upstream speed = 4 km/hr
Speed of boat = 1/2 * (7 + 4) km/hr
5. A boat travels downstream from point A to B and comes back to point C half distance between A and B in 18 hours. If speed of boat is still water is 7 km/hr and distance AB = 80 km, then find the downstream speed.
A) 15 km/hr
B) 18 km/hr
C) 12 km/hr
D) 10 km/hr
E) 6 km/r

Option D
Solution:

A to B is 80, so B to is 80/2 = 40 km
Let speed of current = x km/hr
So 80/(7+x) + 40/(7-x) = 18
Solve, x = 3 km/hr
So downstream speed = 7 + 3 = 10 km/hr
6. A boat can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5 and half hours. What is the speed of the current?
A) 13 km/hr
B) 8 km/hr
C) 7 km/hr
D) 11 km/hr
E) 16 km/hr

Option D
Solution:

Upstream speed in both cases is 20 and 20 resp. Ratio is 20 : 40 = 1 : 2. So let times in both cases be x and 2x
Downstream speed in both cases is 32 and 48 resp. Ratio is 32 : 48 = 2 : 3. So let times in both cases be 2y and 3y
So x + 2y = 3
and 2x + 3y = 5 1/2
Solve both, x = 2, y = 0.5
So upstream speed is = 20/x = 10 km/hr
And downstream = 32/2y = 32 km/hr
So speed of boat is 1/2 * (32-10)
7. Speed of boat in still water is 14 km/hr while the speed of current is 10 km/hr. If it takes a total of 7 hours to row to a place and come back, then how far is the place?
A) 30 km
B) 18 km
C) 24 km
D) 32 km
E) None of these

Option C
Solution:

USE FORMULA:
Distance = total time * [B2 – R2]/2*B
So distance = 7 * [142 – 102]/2*14
Distance = 24 km
8. A man can row a certain distance downstream in 4 hours and return the same distance in 8 hours. If the speed of current is 16 km/hr, find the speed of man in still water.
A) 47 km/hr
B) 48 km/hr
C) 42 km/hr
D) 50 km/hr
E) None of these

Option B
Solution:

Use formula:
B = [tu + td] / [tu – td] * R
B = [8+4] / [8-4] * 16
B = 48 km/hr
9. There are 3 point A, B and C in a straight line such that point B is equidistant from points A and C. A boat can travel from point A to C downstream in 12 hours and from B to A upstream in 8 hours. Find the ratio of boat in still water to speed of stream.
A) 9 : 2
B) 8 : 3
C) 7 : 1
D) 4 : 1
E) 7 : 3

Option C
Solution:

Let speed in still water = x km/hr, of current = y km/hr
Downstream speed = (x+y) km/hr
Upstream speed = (x – y) km/hr
Let AC = 2p km. So AB = BC = p km.
So
2p/(x+y) = 12
And
p/(x-y) = 8
Divide both equations, and solve
x/y = 7/1
10. A boat can row 18 km downstream and back in 8 hours. If the speed of boat is increased to twice its previous speed, it can row same distance downstream and back in 3.2 hours. Find the speed of boat in still water.
A) 9 km/hr
B) 5 km/hr
C) 4 km/hr
D) 8 km/hr
E) 6 km/hr

Option E
Solution:

Let speed of boat = x km/hr and that of stream = y km/hr
So
18/(x+y) + 18/(x-y) = 8
when speed of boat becomes 2x km/hr:
18/(2x+y) + 18/(2x-y) = 3.2
Solve, x= 6 km/hr