A swimmer swims from a point A against a current for 5 minutes and then swims backwards in favour of the current for next 5 minutes and comes to the point B. If AB = 100 metres, the speed of the current (in km per hour) is :

Options

A. 0.4
B. 0.2
C. 1
D. 0.6

Answer

To solve the problem, we need to determine the speed of the current based on the swimmer's movements against and with the current. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( X \) = speed of the swimmer in still water (in km/h)
- \( Y \) = speed of the current (in km/h)

### Step 2: Convert Time to Hours
The swimmer swims for 5 minutes against the current and then 5 minutes with the current. We need to convert these times into hours:
- 5 minutes = \( \frac{5}{60} \) hours = \( \frac{1}{12} \) hours

### Step 3: Calculate Distances
1. **Distance covered against the current (upstream)**:
\[ \text{Distance} = \text{Speed} \times \text{Time} = (X - Y) \times \frac{1}{12} \]

2. **Distance covered with the current (downstream)**:
\[ \text{Distance} = \text{Speed} \times \text{Time} = (X + Y) \times \frac{1}{12} \]

### Step 4: Set Up the Equation
The total distance from point A to point B (AB) is given as 100 meters. The distance covered upstream and downstream can be expressed as:
\[ \text{Distance downstream} - \text{Distance upstream} = AB \]
Substituting the distances we calculated:
\[ \left( (X + Y) \times \frac{1}{12} \right) - \left( (X - Y) \times \frac{1}{12} \right) = 100 \]

### Step 5: Simplify the Equation
Now, we can simplify the equation:
\[ \frac{1}{12} \left( (X + Y) - (X - Y) \right) = 100 \]
This simplifies to:
\[ \frac{1}{12} \left( 2Y \right) = 100 \]
Multiplying both sides by 12:
\[ 2Y = 1200 \]
Dividing by 2:
\[ Y = 600 \text{ meters per hour} \]

### Step 6: Convert to Kilometers per Hour
Since we need the speed in kilometers per hour, we convert:
\[ Y = \frac{600 \text{ meters}}{1000} = 0.6 \text{ km/h} \]

### Final Answer
Thus, the speed of the current is:
\[ \boxed{0.6 \text{ km/h}} \]