Question 1

A motorboat can travel at 10 km/h in still water. It travelled 91 km downstream in a river and then returned to the same place, talking altogether 20 h. The rate of flow of river is?

Accepted Answer

Given, speed of boat = 10 km/h Let speed of flow of river = x km/h ∴ Upstream speed of boat = (10 - x) km/h and downstream speed of boat = = (10 + x) km/h According to question. 91/(10 - x) + 91/(10 + x) = 20 ⇒ 91(10 + x + 10 - x) / (10 - x) (10 + x) = 20 ⇒ 91(20) / 100 - x2 = 20 ⇒ 91 = 100 - x2 ⇒ x2 = 9 ∴ x = 3

Question 2

A boat has to travel upstream 20 km distance from point X of a river to points Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 min 40 s. What is the speed of the boat?

Accepted Answer

Let x be the speed of the boat and y be the speed of the current. Speed upstream = (x - y) km/h Speed downstream = (x + y) km/h According to the question, 20 /(x - y) + 20/(x + y) = 25/36 In this equation, there are two variables but only one equation. So, the value of x cannot be determined.

Question 3

Speed of motorboat in still water is 45 km/h. If the motor travels 80 km along the stream in 1 h 20 min, then the time taken by it to cover the same distance against the stream will be?

Accepted Answer

Let speed of stream be x km/h Given speed of motorboat in still water = 45 km/h ∴ Speed of boat along stream = (45 + x) km/h According to the question, 45 + x = 80 x 11/3 ⇒ 45 + x = 80 x 3 / 4 ⇒ x = 60 - 45 = 15 ⇒ Speed of boat against stream = 45 - 15 = 30 km/h Hence, required time = Distance / Speed = 80 / 30 = (8 x 60)/3 = 160 min = 2 h 40 min

Question 4

A boat's speed in still water is 5km/h. While river is flowing with a speed of 2km/h and time taken to cover a certain distance upstream is 2 h more than time taken to cover the same distance downstream. Find the distance?

Accepted Answer

Let the distance be D km. Speed download = (5 +2) = 7 km/h and speed upstream = (5 -2) = 3 km/h According to the question, D/3 - D/7 = 2 ⇒ 7D - 3D = 21 x 2 ∴ D = (21 x 2)/4 = 10.5 km

Question 5

A boat takes 9 h to travel a distance upstream and taken 3 h to travel the same distance downstream. If the speed of the boat in still water is 4 km/h, then what is the velocity of the stream?

Accepted Answer

Let velocity of the stream be x km/h ∴ Velocity of the boat downstream = (4 + x) km/h and velocity of the boat upstream = (4 - x) km/h According to the question, 3(4 + x) = 9(4 - x) ⇒ 12 + 3x = 36 - 9x ⇒ 12x = 24 ∴ x = 2 km/h

Question 6

A boat running upstream covers a distance of 10 km in 30 min and while running downstream, it covers the same distance in 25 min away and return, then the speed of the water current is?

Accepted Answer

Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h ∴ Speed of the river's current = (24 - 20)/2 = 4/2 = 2 km/h

Question 7

A steamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h, then find the distance between the two ports.?

Accepted Answer

Let the distance between the two ports be x km. Then, speed downstream = x/4 And speed upstream = x/5 ∴ Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2 ⇒ (5x -4x)/40 = 2 ⇒ x/40 = 2 ∴ x = 80 km

Question 8

In a river, the ratio of the speed of stream and speed of a boat in still water is 2 : 5 Again, ratio of the speed of stream and speed of an another boat in still water is 3 : 4. What is the ratio of the speeds of the first boat to the second boat i…

Accepted Answer

For the first boat, Speed of stream : Speed of boat = 2: 5 Let speed of stream be 2x km/h and speed of boat = 5x km/h Similarly, for the second boat Speed of stream be 3y km/h and speed of boat = 4y In both of the conditions, river is same. ∴ 2x = 3y ⇒ x = 3y/2 Thus, required ratio in speeds of boats in still water = Thus, required ratio in speeds of boats in still water = 5x : 4y = (5 x 3)y/2 : 4y = 15 : 8

Question 9

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

Accepted Answer

Let the speed of man and current be U and V km/h, respectively. Speed upstream = (U - V) km/h Speed down stream = (U + V) km/h According to the question, (3 x 60)/(4 x 15) = U - V ⇒ U - V = 3 ......(i) and (3/4) x (60/10) = U + V ⇒ U + V = 9/2 ...(ii) On adding Eqs. (i) and (ii), we get 2U = 3 + 9/2 ⇒ U = 15/4 On putting the value of U in Eq. (ii), we get 15/4 + V = 9/2 V = 9/2 - 15/4 = 18 - 15/4 ⇒ V = 3/4 Hence, speed of man U = 15/4 and Speed of current V = 3/4 Hence, required ratio = 15/4 : 3/4 = 5 : 1

Question 10

A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the water current, respectively?

Accepted Answer

Let boat's rate upstream be U and boat's rate downstream = V According to the question. Distance covered in 528 min = Distance covered in 240 min ⇒ Distance covered in 8 h 48 min = Distance covered in 4 h ⇒ U x 84/5 = V x 4 ⇒ (44 x U)/5 = 4V ⇒ V = (11 x U)/5 ∴ Required ratio = (V + U)/2 : (V - U)/2 ⇒ = (11U/5 + U)/2 : (11U/5 - U)/ 2 ⇒ = 16U/5 : 6U/5 = 8 : 3

Question 11

A motorboat travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the stream is?

Accepted Answer

Let the speed of a boat and stream be U and V km/h ∴ Speed of boat along stream = (U + V) km/h and speed of boat against stream = (U - V) km/h According to the question, 25/(U - V) + 39/(U + V) = 8 ....(i) and 35/(U - V) + 52/(U + V ) = 11 ..(ii) On multiplying Eq. (i) by 4 and Eq. (ii) by 3, then subtract Eq. (ii) from Eq, we get 100/(U - V) - 105/(U - V) = -1 ⇒ 5/(U - V) = 1 ⇒ U - V = 5 ...(iii) On substituting the value of (U - V) = 5 in Eq. (i) we get 25/5 + 39/(U + V) = 8 ⇒ 39/(U + V) = 8 - 5 ⇒ U + V = 39/3 ⇒ U + V = 13 ....(iv) On solving Eqs. (iii) and (iv), we get U = 9 and V = 4 Hence, speed of stream = 4 km/h

Question 12

The speed of a boat in still water is 4 km/hr and the speed of current is 2 km/hr. If the time taken to reach a certain distance upstream is 9 hours, find the time it will take to go same distance downstream?

Accepted Answer

Upstream distance = (4 - 2) x 9 = 18 km ∴ Required time = 18/(4 + 2) = 3 hrs.

Question 13

Ramesh can row a certain distance downstream is 6 hours and return the same distance in 9 hours. If the speed of Ram, Ramesh in still water is 12 km/hr, find the speed of the stream.

Accepted Answer

∵ [(9 + 6)/(9 - 6)] x v = 12 ∴ v = 2.4 km/hr

Question 14

A man rows to a place 48 km distance 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. Find the rate of the stream?

Accepted Answer

Suppose that the man takes H hours to cover 4 km downstream and H house to cover 3 km upstream. Then, 48H/4 + 48H/3 = 14 ⇒ H = 1/2 ∴ Rate upstream = 3/(1/2)= 6 km/hr and rate downstream = 4/(1/2) = 8 km/hr ∴ Rate of the stream = (8 - 6)/2 = 1 km/hr .

Question 15

A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

Accepted Answer

Upstream speed = B-S Downstream speed = B+s B-S = 15/5 = 3 km/h Again B= 4S Therefore B-S = 3= 3S => S = 1 and B= 4 km/h Therefore B+S = 5km/h Therefore, Time during downstream = 15/5 = 3h

Question 16

A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river?

Accepted Answer

Let mans rate upstream be x km/hr. Then his rate downstream is 3 x km/hr Given: Speed in still water = 9 (1/3) = 28/3 km/hr i.e, ½ (a+b) = 28/3 km/hr ½ (x+3x) = 28/3 2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr rate upstream b = 14/3 km/hr and rate downstream a = 14/3 x 3 = 14 km/hr speed of the current = ½ (a-b) = ½ (14  14/3) = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr

Question 17

A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed o…

Accepted Answer

Let the speed of the boat = p kmph Let the speed of the river flow = q kmph From the given data, 2 x 28 p + q = 28 p - q => 56p - 56q -28p - 28q = 0 => 28p = 84q => p = 3q. Now, given that if 28 3 q + 2 q + 28 3 q - 2 q = 672 60 = > 28 5 q + 28 q = 672 60 = > q = 3 kmph = > x = 3 q = 9 kmph Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.

Question 18

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distanc…

Accepted Answer

Speed in downstream = (14 + 4) km/hr = 18 km/hr; Speed in upstream = (14 – 4) km/hr = 10 km/hr. Let the distance between A and B be x km. Then, x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.

Question 19

A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?

Accepted Answer

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by 2 × t 1 × t 2 t 1 + t 2 = 2 × 12 × 24 36 = 16 h

Question 20

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?

Accepted Answer

Speed of the stream = 1 Motor boat speed in still water be = x kmph Down Stream = x + 1 kmph Up Stream = x - 1 kmph [35/(x + 1)] + [35/(x - 1)] = 12 x = 6 kmph

Boats and Streams Questions