All questions of Boats and Stream for Bank Exams Exam

Given ratio of distance = 2:1, let the distance between A and C =2X km and B To C = X km respectively. total dis. travelled A to B= 3X km downstream speed =(9+3)=12 km/hr. upstream Speed =(9-3)= 6km/hr; so, time taken to travel from A to B= 3X/12 hrs. similarly between B to C =X/6 hrs. Total time taken =(3X/12+X/6)= 5X/12 hrs. equating 5X/12= 10, we get X=24 kms. so, the distance between A to B= 3X=(3*24)= 72 kms. op(c)

Given data:
Distance = 48 Km
Speed of stream = 3 Km/hr
Let the speed of the boat in still water be x km/hr

When the boat travels downstream:
Speed of the boat = (x + 3) km/hr
Time taken = distance/speed = 48/(x + 3) hr

When the boat travels upstream:
Speed of the boat = (x - 3) km/hr
Time taken = distance/speed = 48/(x - 3) hr

According to the question,
Time taken downstream - Time taken upstream = 128 min
i.e., 48/(x + 3) - 48/(x - 3) = 128/60
Simplifying this equation, we get:
12x = 169
x = 169/12 = 14.083 km/hr

Therefore, the speed of the boat in still water is 14.083 km/hr, which is closest to option C (12 km/hr).

Analysis:
To solve the problem, we can use the formula:
Speed of boat in still water (B) = 1/2 (Speed downstream + Speed upstream)
Let the speed of the stream be 'S' km/hr.
Given,
Speed of boat in still water (B) = 10 km/hr
Time taken for forward journey (A to B) = Time taken for backward journey (B to A)
Let the distance between A and B be 'D' km.
Let the speed downstream be 'B + S' km/hr and speed upstream be 'B - S' km/hr.
Let the time taken for the forward journey be 't' hrs.
Then,
Time taken for backward journey = t hrs
Distance covered in the forward journey = Distance covered in backward journey = D km
Speed downstream = Distance/Time = D/t km/hr
Speed upstream = Distance/Time = D/t km/hr
Speed downstream = B + S km/hr
Speed upstream = B - S km/hr

Calculation:
Using the formula,
B = 1/2 (B + S + B - S)
10 = 1/2 (2B)
B = 5 km/hr

Substituting B = 5 km/hr in the equations,
D/t = (10 + S) km/hr
D/t = (10 - S) km/hr

Dividing both the equations,
(10 + S)/(10 - S) = 1
10 + S = 10 - S
2S = 0
S = 0

Conclusion:
The speed of the stream cannot be determined as the solution leads to 'S = 0'. This implies that the boat travels in still water and there is no current or stream. Therefore, the answer is option 'E'.

Given information:
- Ratio of speeds of boats A and B in still water = 3:2
- Rate of current = 10 km/hr
- Boat B increases speed by 70% on return journey

To find:
- Speed of Boat A

Approach:
1. Use the concept of relative speed to find the speed of each boat with respect to the water.
2. Use the given ratio of speeds of the two boats to set up equations for their speeds in still water.
3. Use the time taken by each boat to travel from P to Q and back to P to set up equations for the distances traveled.
4. Solve the equations to find the speed of Boat A.

Calculation:
Let the speeds of boats A and B in still water be 3x and 2x, respectively.
Speed of Boat A with respect to the water = Speed of Boat A in still water + Rate of current = 3x + 10
Speed of Boat B with respect to the water = Speed of Boat B in still water + Rate of current = 2x + 10

Let the distance from P to Q be d km.
Time taken by Boat A to travel from P to Q = d / (3x + 10)
Time taken by Boat B to travel from P to Q = d / (2x + 10)
Time taken by Boat B to travel from Q to P with increased speed = d / (2.7x + 10)

Since both boats return to P at the same time, we can set up the following equations:

Time taken by Boat A to travel from Q to P = Time taken by Boat B to travel from Q to P with increased speed
d / (3x - 10) = d / (2.7x + 10)

Solving for x, we get x = 10.
Therefore, the speed of Boat A in still water = 3x = 30 km/hr.

Answer: The speed of Boat A is 30 km/hr, option (b) is correct.