A swimmer can swim at 5 km/hour in still water. When the river flows at 1 km/hour, then he takes 75 minutes to go to a certain point and come back to the starting point. How far is this place?

Correct option is B

Given:

1. Swimmer's speed in still water = 5 km/h

2. River's current speed = 1 km/h

3. Total time taken to go to the point and return = 75 minutes = $$\frac{75}{60}$$​ = 1.25 hours

Formula Used:

The effective speed of the swimmer:

1. While swimming downstream (with the current):

Effective speed downstream = Swimmer's speed in still water + River's current speed

2. While swimming upstream (against the current):

Effective speed upstream = Swimmer's speed in still water - River's current speed

The total distance is calculated as:

Total time = $$\frac{\text{Distance}}{\text{Speed downstream}} + \frac{\text{Distance}}{\text{Speed upstream}}$$​​

Solution:

1. Calculate effective speeds:

- Speed downstream = 5 + 1 = 6 km/h

- Speed upstream = 5 - 1 = 4 km/h

2. Let the one-way distance to the point be d:

​$$\text{Total time} = \frac{d}{6} + \frac{d}{4}$$​​

3. Substitute total time 1.25 hours:

​$$1.25 = \frac{d}{6} + \frac{d}{4}$$​​

4. Find a common denominator and solve for d:

​$$1.25 = \frac{4d + 6d}{24}$$​​

​$$1.25 = \frac{10d}{24}$$​​

1.25 $$\times$$​ 24 = 10d

30 = 10d

d = 3

Final Answer:

The distance to the point is:

3 km