BANK & INSURANCE (BOAT AND STREAM) PART 2

Total Questions: 40

21. Shyam rowed a distance of 24 km in 3 hours in still water. He rowed 20 km in 2 hrs downstream. Find the time he would take to travel 36 km upstream.

Correct Answer: (e) 6 hours
Solution:Speed of boat = 24/3 = 8 km/hr

Downstream speed = 20/2 = 10 km/hr

Stream speed = 10 - 8 = 2 km/hr

Upstream speed = 8 - 2 = 6 km/hr

Time taken to travel 36 km upstream = 36/6 = 6 hr

22. Speed of boat in downstream is (15 + x) km / h. The boat takes 4.5 hours to cover a distance of 30 km each in upstream and downstream. Find the value of x if the speed of the stream is x km / h.

Correct Answer: (e) 5 km / h
Solution:Speed of boat in still water = 15 + x - x = 15 km/h

Distance = 30 km

⇒ [30/(15 + x)] + [30/(15 - x)] = 4.5

⇒ 900/(225 - x²) = 9/2

∴ x = 5

23. A boat sails 10 km upstream at the rate of 3 km/hr. If the stream flows at the rate of 1 km/hr, then how long will the boat take for the return trip?

Correct Answer: (c) 2 hr
Solution:Upstream speed = 3 km/hr and stream speed = 1 km/hr

Speed of boat = 3 + 1 = 4 km/hr

Downstream speed = speed of boat + stream speed

Downstream speed = 4 + 1 = 5 km/hr

Time taken for boat for return trip = 10/5 = 2 hr

24. The speed of boat in still water is 6 km/hr and speed of stream is 3 km/hr. Calculate the time taken to cover 27 km distance downstream and returning on it upstream.

Correct Answer: (d) 12 hr 
Solution:Upstream speed = 6 - 3 = 3 km/hr

Downstream speed = 6 + 3 = 9 km/hr

It has to travel 27 km upstream and downstream both.

Time taken = (27/9 + 27/3) = 3 + 9 = 12 hr

25. The ratio of the speed of a boat in still water and the speed of the stream is 5 : 1. If the speed of travelling downstream is 24 km/hr, then find the time taken by boat to cover 48 km while moving upstream

Correct Answer: (a) 3 hrs 
Solution:Let the speed of the boat in still water and speed of the stream be 5x and x respectively

According to the question,

5x + x = 24

x = 4

Upstream speed = 5x - x = 16 kmph

∴ Required time = 48/16 = 3 hours

26. A boat with a speed of 21 km/hr in still water, travels from point A to B in the downstream direction and returns to point A. Another boat with speed of 28 km/hr travels from B to A and returns to point B. The difference between the time taken by them to cover the distance is 6.5 hrs. What is the distance between points A and B, if the speed of stream is 7 km/hr?

Correct Answer: (e) 210 km
Solution:Speed of first boat from point A to B in downstream direction = 21 + 7 = 28 km/hr

Speed of first boat from point B to A (upstream)

= 21 - 7 = 14 km/hr

Let the distance between A to B = D

Total time taken to complete this distance by first boat

⇒ (D/28) + (D/14) = 3D/28

Speed of second boat from point B to A in upstream direction = 28 - 7 = 21 kmph

Speed of second boat from point A to B (downstream)

= 28 + 7 = 35 km/hr

Total time taken to complete this distance by second boat

⇒ (D/21) + (D/35) = 8D/105

According to question,

(3D/28) − (8D/105) = 6.5

⇒ (45D − 32D)/420 = 6.5

⇒ D = 210

∴ The distance between points A and B is 210 km

27. A boat whose speed is 20 kmph in still water. The same boat goes 60 km downstream and the same distance upstream in 8 hours. Find the total time taken by boat to travel 30km downstream and 40km upstream

Correct Answer: (b) 8 hours 
Solution:Let the speed of the stream be A kmph.

⇒ 60/(20 + A) + 60/(20 − A) = 8

⇒ 300 - 15A + 300 + 15A = 2(400 - A²)

⇒ 300 = 400 - A²

⇒ A = 10 kmph

Downstream speed = 20 + 10 = 30 kmph

Upstream speed = 20 − 10 = 10 kmph

∴ Total time = 30/30 + 40/10 = 1 + 4 = 5 hours

28. A boat moves upstream at a speed of 12km/hr and covers a distance of 144 km. If the rate of flow of the stream is 4km/hr, the time taken by the boat to move downstream is:

Correct Answer: (b) 7 hrs 12 mins 
Solution:Let the speed of the boat in still water be x.

The speed of the boat upstream = 12 km/hr = x − Rate of flow of stream = x − 4

So, x = 16 km/hr

Speed of the boat downstream = 16 + 4 = 20 km/hr

Distance to be covered = 144 km

So, Time taken = Distance/Speed = 144/20 = 7.2 hours = 7 hrs 12 mins

29. Two boats are sailing in a river in same directions with different speeds. First boat takes 5 hrs more than the 2nd one to travel the same distance in downstream. Speed of the current is 2 km/hr. Find the distance if the sum of speeds of the boats in still water is 20 km/hr and product of speeds in still water (in km/hr) is 64 km/hr.

Correct Answer: (b) 45 km 
Solution:Let speed of slower and faster boat in still water be x and y respectively.

Given, x + y = 20 …..(1) And xy = 64 …..(2)

By equation (1) and (2),

we get: x = 4 km/hr, y = 16 km/hr

Let distance be D km.

According to question,

D/(4+2) - D/(16+2) = 5

⇒ 3D/18 - D/18 = 5

⇒ D/9 = 5

⇒ D = 45

30. A boat can travel 77 km in upstream in 165 minutes and the speed of the stream is 12.5% of the speed of the boat in still water. Find the time taken by the boat to travel 81 km in downstream.

Correct Answer: (b) 135 minutes
Solution:Let the speed of the boat in still water be ‘8x’ km/h

Then, speed of the stream = 8x × 0.125 = x km/h

So, upstream speed of the boat = 8x - x = ‘7x’ km/h

So, 7x = 77 ÷ (165 ÷ 60)

7x = 77 ÷ 27.5

7x = 28

x = 28 ÷ 7 = 4

So, downstream speed of the boat = 8x + x = 9x

= 9 × 4 = 36 km/h

So, time taken by the boat to travel 81 km downstream = 81 ÷ 36 = 2.25 hours

= 2.25 × 60 = 135 minutes