Question 1

Ashutosh can row 24 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream.?

Accepted Answer

Let rate of stream be 'a' km/h. According to the question. 24 + a = 2(24 - a) ⇒ 24 + a = 48 - 2a ⇒ 3a = 48 - 24 = 24 ∴ a = 24/3 = 8 km/h

Question 2

A boat goes 12 km in 1 h in still water. It takes thrice time in covering the same distance against the current. Find the speed of the current.?

Accepted Answer

Speed of a boat in still water = distance / time = 12/1 = 12 km/h Speed against the current = 12/3 km/h Let the speed of the current = x km/h According to the question, 12 - x = 4 ⇒ x = 8 km/h

Question 3

A boatman takes twice as long to row a distance against the stream as to row the same distance with the stream. Find the ratio of speeds of the boat in still water and the stream.?

Accepted Answer

Let boatman's speed upstream x And his speed downstream = 2x ∴ Ratio = (Speed in still water) : (Speed of stream) = (2x + x/2) : (2x - x/2) = 3x/2 : x/2 = 3 : 1

Question 4

A river is flowing with a steady speed of 4 km/h. One rows his boat downstream in the river and then returns by rowing upstream in the same river. When he returns to the starting points, the total distance covered by him is 42 km. If the return jour…

Accepted Answer

Let the speed of rowing in still water be u km/h. Distance in downstream motion = 21 km and speed downstream = (u + 4) km/h ∴ Time taken = 21/ (u + 4) Distance upstream motion = 21 km and speed upstream = (u +4) km ∴ Time taken = 21/(u - 4) According to the question. 21/(u + 4) + 2 = 21/(u - 4) ⇒ (21 + 2u + 8)/u + 4 = 21/(u - 4) ⇒ (2u + 29)/(u + 4) = 21/(u - 4) ⇒ (u - 4) (2u + 29) = 21(u + 4) ⇒ 2u2 - 8u + 29u - 116 = 21u + 84 ⇒ 2u2 + 21u - 116 = 21u + 84 ⇒ 2u2 = 84 + 116 ⇒ u2 = 200/2 ⇒ u2 = 100 ⇒ u = 10 km/h

Question 5

A river is flowing at a speed of 5 km/h in a particular direction. A man, who can swim at a speed of 20 km/h in still water, starts swimming along the direction of flow of the river from from points A and reaches another point B which is at a distan…

Accepted Answer

Given, Speed of the stream = 5 km/h and speed of the man in still water = 20 km/h ∴ Speed of the man downstream = 20 + 5 = 25 km/h and speed of the man upstream = 20 - 5 = 15 km/h ∴ Total time taken to complete the whole journey = 30/25 + 30/15 = (30 x 8) / 75 = 3 h 12 min

Question 6

Ishwar is rowing a boat. He takes half time in moving a certain distance downstream than upstream. What is the ratio of the rate of boat in still water to the rate of current?

Accepted Answer

Let speed of Ishwar's boat in still water be x km/h and speed of current = y km/h Rate downstream = (x + y) km/h Rate upstream = (x - y) km/h Let the distance covered in each case be a. According to the question, 2a/(x + y) = a/(x - y) ⇒ 2(x - y) = x + y 2x - 2y = x + y ⇒ x = 3y ∴ x/y = 3/1 ⇒ x : y = 3 : 1

Question 7

A man can row 7 1/ 2 km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place?

Accepted Answer

Let the distance be L km. Speed of the main in still water = 71/2 km/h and speed of the river = 15 km/h ∴ Speed of the man downstream = 7.5 + 1.5 = 9 Speed of the man upstream = 7.5 - 1.5 = 6 km/h According to the question, L/9 + L/6 = 50/60 ⇒ (4L + 6L)/36 = 50/60 ⇒ 10L/36 = 50/60 ⇒ L = (50 x 36)/(10 x 60) 5⇒ x = 3 km

Question 8

The ratio of speed of a motorboat to that of the current of water is 35 : 5. The motorboat goes along with the current in 5 h 10 min. Find the time to come back of motorboat?

Accepted Answer

Let speed of a motorboat be = 36k km/h and speed of the current = 5k km/h ∴ Speed downstream = (36 + 5)k = 41k km/h and speed upstream = (36 - 5)k = 31k km/h Let distance be D km. According to the question When boat goes along with the current. Distance = Time x Speed ⇒ D = (5 + 10/60) x 41k ⇒ D = 31/6 x 41k ....(i) Again, when boat come back a = Time x Speed From Eq. (i) . 31/6 x 41k = Time x 31k ⇒ Time = 41/6 Time = 6 h 50 min.

Question 9

Ravi can row downstream at 9 km/h and upsteam at 5 km/h. Find the speed of Ravi in still water and speed of current.

Accepted Answer

Given, downstream speed = 9 km/h and upstream speed = 5 km/h According to the formula Ravi's speed in still water = (Speed downstream + Speed upstream )/2 = 1/2(9 + 5) = 14/2 = 7 km/h and speed of current = (Speed downstream - Speed upstream)/2 = (9 - 5)/2 = 4/2 = 2 km/h.

Question 10

A boatman row 1 km in 5 min along the steam and 6 km in 1 h against the stream. The speed of the steam is?

Accepted Answer

Let the speed of boat and steam be x and y km/h. ∴ Speed of boat along steam = (x + y) km/h and speed of boat against stream = (x - y) km/h According to the question, x + y = 1 / (5/60) = 60/5 ⇒ x + y = 12 ...(i) and y - x = 6 ...(ii) On adding Eqs. (i) and (ii), we get 2x = 18 x = 18/2 = 9 On putting the value of x in Eq. (i), We get 9 + y = 12 y = 12 - 9 = 3 Hence, speed of boat = 9 km/h and speed of steam = 3 km/h

Question 11

A man 8 km/hr in still water. If the river is running at 2 km/hr, it taken 32 minutes to row to a place and back. How for is the place?

Accepted Answer

∵ D/(8 - 2) + D/(8 + 2) = 32/60 ⇒ D/6 + D/10 = 32/60 ⇒ 10D + 6D = 32 ∴ D = 2 km

Question 12

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 1/ 2 hours. The velocity of the current is?

Accepted Answer

Let the speed upstream be U km/hr and the speed downstream be V km/hr respectively. Then 24/U + 36/V = 6 ...(i) and 36/U + 24/V = 13/2 ...(ii) Solving these 2 equations we get ∴ U = 8 km/hr and V = 12 km/hr ∴ Velocity of current = (12 - 8)/2 km/hr = 2 km/hr

Question 13

A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9km/hr and the speed of the current is 3 km/hr the distance between A and B is?

Accepted Answer

Speed downstream = (9 + 3) km/hr = 12km/hr Speed upstream = = (9 - 3) km/hr = 6km/hr Let the distance AB = d km Then, d/6 + d/12 = 3 ⇒ 2d + d = 36 ⇒ d = 12 ∴ Distance AB = 12 km

Question 14

A man can swim 3 km/hr in still water. If the velocity of the stream be 2 km/hr, the time taken by him to swim to a place 10 km upstream and back is?

Accepted Answer

Speed upstream = (3 - 2) km/hr = 1 km/hr Speed downstream = (3 + 2) km/hr = 5 km/hr Total time taken = (10/1 + 10/5) hr = 12 hrs.

Question 15

A man can row three quarters of a kilometre against the stream in 11 1/ 4 minutes and return in 7 1/ 2 minutes. The speed of the man in still water is?

Accepted Answer

Speed upstream = (3/4) x (4/45 x 60 km/hr = 4 km/hr Speed upstream = (3/4) x (2/15) x 60 km/hr = 6 km/hr ∴ Speed in still water = (4 + 6)/2 km/hr = 5 km/hr

Question 16

A man can row 9 1/ 3 in still water and he finds that it takes him thrice as much time to row up than as to row down the same distance in river. The speed of the current is?

Accepted Answer

Let speed upstream = x km/hr Then, speed downstream = 3x km/hr ∴ Speed in still water = (x + 3x)/2 km/hr = 2x km/hr Speed of the current = (3x - x)/2 km/hr = x km/hr &becaus 2x = 28/3 ∴ x = 14/3 = 42/3 km/hr.

Question 17

The current of a stream runs at 1 km/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?

Accepted Answer

Let the speed in still water be x km/hr ∵ 35/(x - 1) + 35/(x + 1) = 12 ⇒ 35(2x) = 12(x2 - 1) ⇒ 12x2 - 70x - 12 = 0 ⇒ 12x2 - 72x + 2x - 12 = 0 ⇒ 12x(x - 6) + 2 (x - 6) = 0 ⇒ (x - 6) (12x + 2) = 0 ∴ x = 6 km/hr

Question 18

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?

Accepted Answer

Suppose he moves 4 km downstream in H hrs. Then, Speed downstream = 4/H km/hr Speed upstream = 3/H km/hr T1 + T2 = 14 ∵ (48 x H)/4 + (48 x H)/3 = 14 ⇒ 12H + 16H = 14 ⇒ H = 1/2 ∴ Speed downstream = 8 km/hr Speed upstream = 6 km/hr ∴ Rate stream = (8 - 6)/2 km/hr = 1 km/hr

Question 19

Speed of a boat in standing water is 6 km/hr and the speed of the stream is 1.5 km/hr. A man rows to a place at a distance of 22.5 km and comes back to the starting point. The total time taken by him, is?

Accepted Answer

Speed upstream = (6 - 1.5) km/hr = 4.5 km/hr Speed downstream = (6 + 1.5) km/hr = 7.5 km/hr Total time taken = (22.5/4.5 + 22.5/7.5) hrs = (5 + 3) hrs. = 8 hrs.

Question 20

A boat takes 3 hours to travel from place M to N downstream and back from N to M upstream. If the speed of the boat in still water is 4 km, what is the distance between the two places?

Accepted Answer

Let the distance between M and N and the speed of current be d km and x km/hr respectively. According to the question = {d/(4 + x) + d/(4 - x)} = 3 In the above equation we have only one equations but two variables. Hence cannot be determined (Data inadequate).

Boats and Streams Questions