Question 1

A boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?

Accepted Answer

Speed of Boy is B = 4.5 kmph Let the speed of the stream is S = x kmph Then speed in Down Stream = 4.5 + x speed in Up Stream = 4.5 - x As the distance is same, => 4.5 + x = (4.5 - x)2 => 4.5 + x = 9 -2x 3x = 4.5 x = 1.5 kmph

Question 2

A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the strin…

Accepted Answer

Let the distance covered be D km. D 10 + 4 + D 10 - 4 = 5 D 14 + D 6 = 5 10D = 42 x 5 = 210 => D = 21 km

Question 3

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

Accepted Answer

Speed of the boat downstream s=a/t= 60/3 = 20 kmph Speed of the boat upstream s= d/t = 30/3= 10 kmph Therefore, The speed of the stream = s p e e d o f d o w n s t r e a m - s p e e d o f u p s t r e a m 2 =5 kmph

Question 4

A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?

Accepted Answer

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr. Speed in downstream = 3 x 60/18 = 10 km/hr Rate of current = (10-9)/2 = 1/2 km/hr.

Question 5

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?

Accepted Answer

Speed in still water = 6 kmph Stream speed = 1.2 kmph Down stream = 7.2 kmph Up Stream = 4.8 kmph x/7.2 + x/4.8 = 1 x = 2.88 Total Distance = 2.88 x 2 = 5.76 kms

Question 6

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Accepted Answer

Let the speed of the boat upstream be p kmph and that of downstream be q kmph Time for upstream = 8 hrs 48 min = 8 4 5 hrs Time for downstream = 4 hrs Distance in both the cases is same. => p x 8 4 5 = q x 4 => 44p/5 = 4q => q = 11p/5 Now, the required ratio of Speed of boat : Speed of water current = q + p 2 : q - p 2 => (11p/5 + p)/2 : (11p/5 - p)/2 => 8 : 3

Question 7

A boat whose speed in still water is 9 kmph, goes 12 km downstream and comes back in 3 hrs. Find the speed of the stream?

Accepted Answer

Let the speed of the stream = x kmph From the given data, 12 9 + x + 12 9 - x = 3 h r s 3 x 2 = 27 => x = 3 kmph Therefore, the speed of the stream = 3 kmph

Question 8

A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by

Accepted Answer

Let the distance be d. d 8 - 2 - d 8 + 2 = 4 => 2d = 120 => d = 60 kms.

Question 9

A motorboat can go 10 miles downstream on a river in 20 min. It takes 30 min for this boat to go back at the same 10 miles. Find the speed of the current ?

Accepted Answer

As the distance travelled is constant, the time taken is inversely proportional to speed. Let 'u' be the speed of the current and 'v' be the speed of the boat. Speed of the boat downstream = v + u & upstream = v - u => v+u/v-u = 30/20 => v/u = 5 => v = 5u => v + u = 6u = 10/20/60 miles/hr => 6u = 30 m/h => u = 5 m/h

Question 10

In one hour, a boat goes 12 km/hr along the stream and 6 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

Accepted Answer

Speed in still water = Average of Speed in Upstream and speed in Downstream = 1/2 (12 + 6) kmph = 9 kmph.

Question 11

If sum of upstream and downstream speed of a boat is 82 kmph, and the boat travels 105 km. upstream in 3 hr, Find the time taken by boat to cover 126 km downstream.

Accepted Answer

Let Speed of boat in still water = b Let Speed of still water = w Then we know that, Speed of Upstream = U = boat - water Speed of Downstream = D = boat + water Given, U + D = 82 b - w + b + w = 82 2b = 82 => b = 41 kmph From the given data, 41 - w = 105/3 = 35 w = 6 kmph Now, b + w = 126/t => 41 + 6 = 126/t => t = 126/47 = 2.68 hrs.

Question 12

A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?

Accepted Answer

Downstream speed = 72km/8hrs = 9 kmph upstream speed = 84km/12hrs = 7 kmph speed of boat = avg of downstream and upstream speeds speed of boat = (9+7)/2kmph = 8 kmph. current speed = half of the difference of downstream and upstream speeds currend speed = (9-7)/2kmph = 1 kmph

Question 13

A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?

Accepted Answer

Speed in downstream = 96/8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12 – 4 = 8 kmph Speed in upstream = 8 – 4 = 4 kmph Time taken to cover 8 km upstream = 8/4 = 2 hours.

Question 14

Rajesh rows in still water with a speed of 4.5 kmph to go to a certain place and comes back. Find his average speed for the whole journey, if the river is flowing with a speed of 1.5 kmph?

Accepted Answer

Let the distance in one direction = k kms Speed in still water = 4.5 kmph Speed of river = 1.5 Hence, speed in upstream = 4.5 - 1.5 = 3 kmph Speed in downstream = 4.5 + 1.5 = 6 kmph Time taken by Rajesh to row upwards = k/3 hrs Time taken by Rajesh to row downwards = k/6 hrs Now, required Average speed = Total distance Total speed = 2 k k 3 + k 6 = 2 k x 18 6 k + 3 k = 4 kmph Therefore, the average speed of the whole journey = 4kmph.

Question 15

Find the speed of stream if a boat covers 36 km in downstream in 6 hours which is 3 hours less in covering the same distance in upstream?

Accepted Answer

Speed of the boat upstream = 36/9 = 4 kmph Speed of the boat in downstream = 36/6 = 6 kmph Speed of stream = 6-4/2 = 1 kmph

Question 16

A man can row against the current three fourth of a kilometer in 15 min and returns same distance in 10 min, then ratio of his speed to that of current?

Accepted Answer

Let the speed of the man in still water = p kmph Speed of the current = s kmph Now, according to the questions (p + s) x 10 = (p - s) x 15 2p + 2s = 3p - 3s => p : s = 5 : 1 Hence, ratio of his speed to that of current = 5:1.

Question 17

A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?

Accepted Answer

72 --- 9 ? ---- 1 => Down Stream = 8 45 ---- 9 ? ---- 1 => Up Stream = 5 Speed od current S = ? S = (8 - 5)/2 = 1.5 kmph.

Question 18

A person can row 8 1/2 km an hour in still water and he finds that it takes him twice as long to row up as to row down the river. The speed of the stream ?

Accepted Answer

Given speed of the person = 8 1/2 = 17/2 kmph Let the speed of the stream = x kmph speed of upstream = 17/2 - x speed of downstream = 17/2 + x But given that, 2(17/2 - x) = 17/2 + x => 3x = 17/2 => x = 2.83 kmph.

Question 19

Amith can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream for Amith ?

Accepted Answer

Let the speed of boat and stream be x and y kmph respectively. According to question d/x+y + d/x-y = 5h 15m or 21/4 hrs ......(i) and 2d/x-y = 7...... (ii) From eq. (i) and (ii) 2d/x+y = 7/2 Hence, Amith will take to row 2d km distance downstream in 7/2 hrs = 3.5 hrs = 3 hrs 30 min.

Question 20

A motorboat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the motorboat and speed of the water current respectively?

Accepted Answer

8:3

Boats and Streams Questions