Question 1

A swimmer's speed downstream is 11 km/h and speed of the stream is 1.5 km/h. Find the upstream speed of swimmer.?

Accepted Answer

Rate of stream = ( Speed downstream - Speed upstream )/2 ⇒ 1.5 = (11 - Speed upstream)/2 ⇒ 11 - Speed upstream = 3 ∴ Speed upstream = 11 - 3 = 8 km/h

Question 2

A boat goes 48 km downstream in 20 h. It takes 4 h more to cover the same distance against the stream. What is the speed of the boat in still water?

Accepted Answer

Speed downstream = 48/20 = 2.4 km/h Speed upstream = 48/24 = 2 km/h ∴ Speed of boat in still water = (Speed downstream + Speed upstream)/2 = (2.4 + 2)/2 = 4.4/2 = 2.2 km/h

Question 3

Keshav can row 60 km downstream and 36 km upstream, taking 10 h each time. What is the velocity of the current?

Accepted Answer

Speed upstream = Distance/Time = 60/10 = 6 km/h Speed upstream = Distance/Time = 36/10 = 3.6 km/h ∴ Velocity of the current = (speed downstream - Speed upstream)/2 = (6 - 3.2)/2 = 1.2 km/h

Question 4

What time will be taken by a boat to cover a distance of 128 km along the stream, if speed of a boat in still water is 24 km/h and speed of stream is 8 km/h?

Accepted Answer

Downstream speed of boat = Speed of boat in still water + Speed of stream = 24 + 8 = 32 km/h ∴ Required time = Distance/Speed downstream = 128/32 = 4 km/h

Question 5

A boat goes 12 km upstream in 48 minutes. The speed of stream is 2 km/hr. The speed of boat in still water is?

Accepted Answer

∵ (12 x 60)/48 = (L - 2) ∴ L = 15 + 2 = 17 km/hr

Question 6

The current of a stream runs at the rate of 4 km/hr. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is?

Accepted Answer

Let the speed in still water be x km/hr Then, 6/x + 4 + 6/x - 4 = 2 ⇒ 6[ x - 4 + x + 4] = 2(x2 - 16) ⇒ x2 - 6x - 16 = 0 ⇒ (x - 8) (x + 2) = 0 ∴ x = 8 km/hr

Question 7

A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes. The speed of the current is?

Accepted Answer

Speed upstream = 6 km/hr Speed downstream = 10 km/hr ∴ Speed of the current = (10 - 6)/2 km/hr = 2 km/hr

Question 8

A man rows upstream 16 km and downstream 28 km talking 5 hours each time. The velocity of the current is?

Accepted Answer

Speed downstream = (28/5) km/hr = 5.6 km/hr Speed upstream = (16/5) km/hr = 3.2 km/hr Velocity of current = (5.6 - 3.2)/2 km/hr = 1.2 km/hr

Question 9

A man can row at 5 km/hr in still water and the velocity of current is 1 km/hr. It takes him 1 hour to row to a place and back. How far is the place?

Accepted Answer

Speed downstream = (5 + 1) km/hr = 6 km/hr Speed upstream = (5 - 1) km/hr = 4 km/hr Let the required distance be d km Then, d/6 + d/4 = 1 ⇒ 2d + 3d = 12 ∴ d = 2.4 km

Question 10

A man can row 44 km downstream in 4 hours. If the man's rowing rate in still water is 8 km/hr, then find in what time will he cover 25 km upstream?

Accepted Answer

∵ Man's rate in still water = (man's rate with current + his rate against current)/2 ⇒ 8 = 1/2 [ 44/4 + 25/T ] ⇒ 16 = 11 + 25/T ∴ T = 5 hours

Question 11

A boat's man goes 48 km downstream in 8 hours and returns back in 12 hours. Find the speed of the boat in still water and the rate of the stream?

Accepted Answer

Rate downstream = 48/8 = 6 km/hr Rate upstream = 48/12 = 4 km/hr ∴ Speed of boat in still water = (6 + 4)/2 = 5 km/hr Rate of stream = (6 -4)/2 = 1 km/hr

Question 12

A man can row 60 km downstream in 6 hours. If the speed of the current is 3 km/hr, then find in what time will he be able to cover 16 km upstream?

Accepted Answer

Downstream speed = 60/6 = 10 km/hr Speed of stream = 3 km/hr Upstream speed = 10 - (2 x 3) = 4 km/hr ∴ Required time = 16/4 = 4 hours.

Question 13

speed of a boat in standing water is 7 km/hr and the speed of the stream is 1.5 km/hr. A distance of 7.7 km. going upstream is covered in?

Accepted Answer

Upstream speed = 7 - 1.5 = 5.5 km/hr ⇒ 5.5 x T = 7.7 ∴ T = 77.7 / 5.5 = 1hr. 24 minutes

Question 14

A sailor sails a distance of 48 km along the flow of a river in 8 h. If it takes 12 h to return the same distance, then the speed of the flow of the river is?

Accepted Answer

Let speed of the flow of water be x km/h and rate of sailing of sailor be y km/h. Downstream speed (x + y) = 48/8 ⇒ x + y = 6 ....(i) and upstream speed x - y = 4 ...(ii) On solving Eqs. (i) and (ii), we get y = 1 km/h

Question 15

Sameer can row a certain distance downstream in 24 h and can come back covering the same distance in 36 h. If the stream flows at the rate of 12 km/h, find the speed of Sameer in still water?

Accepted Answer

Let the speed of Sameer in still water be x km/h Sameer's speed downstream = (x + 12) km/h Sameer's speed upstream = (x - 12) km/h According to the question, 24(x + 12) = 36(x - 12) ⇒ 2x + 24 = 3x - 36 ⇒ x = 36 + 24 = 60 km/h

Question 16

Pawan can row 24 km/h in still water. When the river is running at 4.8 km/h, it takes him 1 h to row to a place and to come back. How far is the place?

Accepted Answer

Pawan's speed downstream = 24 + 4.8 = 28.8 km/h Pawan's speed upstream = 24 - 4.8 = 19.2 km/h Let the required distance be x. According to the question. x/28.8 + x/19.2 = 1 ⇒ (19.2x + 28.8x) / 552.96 = 1 ⇒ 19.2x + 28.8x = 552.96 ⇒ 48x = 552.96 ∴ x = 552.96/48 = 11.52 km

Question 17

A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 h more in upstream than in the downstream for the same distance. The distance is?

Accepted Answer

Let total distance be x km. According to the question, x/(6 + 2) + 3 = x/6 - 2 ⇒ x/8 + 3 = x/4 ⇒ x/4 - x/8 = 3 ⇒ 2x - x/8 = 3 ∴ x = 8 x 3 = 24 km

Question 18

The speed of the current is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 min. The speed, (in km/h) of the motorboat in still water is?

Accepted Answer

Let speed of boat be x km/h. Given speed of current = 5 km/h ∴ Upstream speed of boat = (x -5) km/h Downstream speed of boat = (x + 5) km/h According to the question. 10/(x - 5) + 10/(x + 5) = 50/60 ⇒ 10(x + 5 + x - 5)/( x2 - 25) = 5/6 ⇒ x2 -24x - 25 = 0 ⇒ x2 - 25x + x - 25 = 0 ⇒ (x - 25) (x + 1) = 0 ∴ x = 25 [∴ x ≠ -1]

Question 19

A boat cover a distance of 30 km downstream in 2 h while it takes 6 h to cover the same distance distance upstream. What is the speed of the boat (in km/h)?

Accepted Answer

Speed of boat downstream = Distance covered / Time taken = 30/2 = 15 km/h Now, speed of boat upstream = Distance covered / Time taken = 30/6 = 5 km/h Now, speed of boat = (Speed download + Speed upstream) / 2 = (15 + 5) / 2 = 10 km/h

Question 20

A man can row at 10 km/h in still water. If he takes total 5 h to go to a place 24 km away and return, then the speed of the water current is?

Accepted Answer

Let speed of water current be x km/h ∴ Speed downstream = (10 + x) km/h. Speed upstream = (10 - x) km/h According to the question, 24/(10 + x) + 24/(10 - x) = 5 ⇒ 24[10 - x + 10 + x] = 5(102 - x2) ⇒ 100 - x2 = (24 x 20) / 5 ⇒ 100 - x2 = 96 ⇒ x2 = 4 ⇒ x = √4 = 2km/h

Boats and Streams Questions