Q 1-The speed of a boat in still water is 8 kmph. If it can travel 1 km upstream in 1 hr, what time it would take to travel the same distance downstream?

A - 1 minute

B - 2 minute

C - 3 minute

D - 4 minute

Answer - D

Explanation

"Speed of the boat in still water = 8 km/hr

Speed upstream = 1 km/hr

Speed of the stream = 8-1 = 7 km/hr

Speed downstream = (8+7) = 15 km/hr

Time taken to travel 1 km downstream =1/15hr = (1×60)/15= 4 minutes"

Q 2-a boat takes 2 times as long to row a distance upstream as to row the same distance downstream. of the river flows at the rate 1 km/hr the speed of the boat in still water is?

A - 6 km/hr

B - 5 km/hr

C - 3 km/hr

D - 4 km/hr

Answer - C

Explanation

"Time taken to travel upstream : time taken to travel downstream = 2 : 1 
speed upstream : speed downstream = 1 : 2 
(as speed is inversely proportional to time when distance is constant) 
Let speed upstream= x and speed downstream = 2x 
Rate of the stream = (2x-x)/2 =x/2 x/2 is given as 1 km/hr 
=> x = 2km/hr 
Speed of the board in still water = 1/2 (2x+x) = 3x/2 = 6/2 = 3 km/hr
"

Q 3-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?

A - 22 km/hr

B - 12 km/hr

C - 20 km/hr

D - 16 km/hr

Answer - A

Explanation

"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 =55/60 hour =11/12 hour ⇒10/(x−2)+10/(x+2)=11/12 120(x+2)+120(x−2)=11((x^2)-4) 240x=11x^2-44 11x^2−240x-44=0 11x^2-242x+2x-44=0 11x(x-22)+2(x-22)=0 (x-22)(11x+2)=0 x=22 or -2/11
 Since x cannot be negative, x = 22 
i.e., speed of the boat in still water = 22 km/hr
"

Q 4-The speed of a boat in still water is 50 kmph. If it can travel 20 km upstream in 1 hr, what time it would take to travel the same distance downstream?

A - 22 minutes

B - 30 minutes

C - 40 minutes

D - 8 minutes

Answer - D

Explanation

"Speed of boat in still water = 50 km/hr

Speed upstream =20 km/hr

Speed of the stream = (50-20) = 25 km/hr

Speed downstream = (50+25) = 75 km/hr

Time taken to travel 10 km downstream 
=10/75hours
=(10×60)/75=8 minutes
"

Q 5-Find the ratio between the speeds of the boat and stream if the boat can travel 30 km upstream in 3 hours and the same distance downstream in 2 hours.

A - 5:1

B - 3:2

C - 4:1

D - 2:3

Answer - A

Explanation

"u = 10 kmph

d = 15 kmph

s = (d-u)/2 = 2.5 kmph         

b = (d+u)/2 = 12.5 kmph

b:s = 5:1"

Q 6-The effective speed of travel of a boat downstream is 18 kmph whereas it is 10 kmph upstream. What is the speed of the current?

A - 14 kmph

B - 8 kmph

C - 4 kmph

D - 5 kmph

Answer - C

Explanation

"Speed of the current

= (d-u)/2

= (18-10)/2

= 4 kmph"

Q 7-"Find the speed of the boat in still water, If a boat covers a certain distance downstream in 1 hour, while it comes back in 11/2 hours. If the speed of the stream be 5 kmph."

A - 12 kmph

B - 18 kmph

C - 25 kmph

D - 22 kmph

Answer - 3

Explanation

"Let the speed of the boat in still water be x kmph. 
Then, Speed downstream = (x + 5) kmph,
 Speed upstream = (x - 5)kmph. (x + 5) * 1 = (x -5) * 3/2 =2x + 10 = 3x - 15 = 25 kmph.
"

Q 8-"The speed of a boat in still water is 30 km/hr and the rate of current
is 6 km/hr the distance traveled downstream in 12 minutes is :"

A - 1.4 km

B - 3.8 km

C - 7.2 km

D - 3.6 km

Answer - C

Explanation

"Speed downstream = (30+ 6) kmph = 36 kmph.

Distance traveled = [36 * 12/60] km = 7.2 km."

Q 9-The speed of a boat in still water is 40 kmph and the speed of the stream is 10 kmph. The distance travelled upstream in 20 minutes is

A - 15 km

B - 10 km

C - 3 km

D - 5 km

Answer - B

Explanation

"u = 30kmph

Distance = 30*20/60 = 10 km"

Q 10-John can row at a speed of 6.8 kmph in still water. If the speed of the stream is 3.2 kmph, find the time taken by him to row 15 km downstream.

A - 1 hour

B - 1.5 hours

C - 150 minutes

D - 180 minutes

Answer - B

Explanation

"Downstream speed

= 6.8+3.2

= 10 kmph

Time taken

= 15/10

= 1.5 hours"

Q 11-A swimmer covers a distance of 28 km against the current and 40 km in the direction of the current. If in each case he takes 4 hours, then the speed of the current is

A - 3 kmph

B - 1.5 kmph

C - 4.5 kmph

D - 8.5 kmph

Answer - B

Explanation

"Let the swimmer's speed be x kmph and 

the speed of the current be c kmph.

Time taken to travel 28 km upstream

= 28/u

= 28/(x-c) = 4

x-c = 28/4 = 7     ------ (I)

Time taken to travel 40 km downstream

= 40/(x+c) = 4

x+c = 40/4 = 10  ------(II)

Solving,

c=1.5 kmph"

Q 12-The current of a stream runs at a rate of 1.5 kmph. A man rows 10 km to an island and returns back immediately. If he can row 4.5 km with the stream in the same time as 3 km

A - 4.5 hours

B - 3 hours

C - 259 minutes

D - 2(7/9) hours

Answer - D 

Explanation

"Speed is inversely proportional to time. 
Hence, upstream speed = 3
Downstream speed = 3d(b-s) = 3d(b+s) 
1.5b = 7.5s = 7.5*1.5 b = 7.5kmph 
u = 6 kmph d = 9 kmph 
Time taken to travel 10 km upstream = 10/u = 5/3 
Time taken to travel 10 km downstream = 10/d = 10/9 
Total time = 25/9 hours = 2(7/9) hours
"

Q 13-The current of a stream runs at the rate of 2.5 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 100 mins. Find the speed of the motor boat

A - 15 kmph

B - 12.5 kmph

C - 10 kmph

D - 7.5 kmph

Answer - B

Explanation

Time taken to travel 10 km upstream

= 10/(b-s)

Time taken to travel 10 km downstream

= 10/(b+s)

[10/(b-2.5)]+[10/(b+2.5)] = 100/60

(b+2.5)+(b-2.5) = (1/6)*(b²-6.25)

b²-12b-6.25 = 0

(b-12.5)(b+0.5) = 0

b=12.5 kmph

Q 14-When a boat travels upstream from A to B hours and returns back to A it takes 5. If the speeds of the boat and the stream are 10kmph and 2 kmph respectively, find the distance

A - 20 km

B - 25 km

C - 24 km

D - 18 km

Answer - C

Explanation

"Let the distance between A and B be x km.

u = b-s = 8 kmph

d = b+s = 12 kmph

(x/u)+(x/d) = 5

(x/8)+(x/12)=5

Solving, x = 24km"

Q 15-A man can row upstream at a speed of 40 kmph and downstream at a speed of 54 kmph. Find the speed of the stream.

A - 2.5 kmph

B - 3.5 kmph

C - 7 kmph

D - 23.5 kmph

Answer - C

Explanation

"Let the speed of the stream be s kmph and the speed of the boat be b kmph.

b+s = 54

b-s = 40 

Solving the equations, s = 7 kmph"

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