Manoj starts swimming in upstream from point P after 12 sec he swims back towards point P and after 12 sec he reaches at point Q.
If distance between P and Q is 144 meters find speed of current?

Options

A. 8 m/s.
B. 6 m/s.
C. 11 m/s
D. 12 m/s

Answer

To solve the problem step by step, we will analyze the situation involving Manoj swimming upstream and downstream.

### Step 1: Understand the scenario
Manoj swims upstream for 12 seconds and then swims back downstream for another 12 seconds. The total distance between points P and Q is given as 144 meters.

### Step 2: Define the variables
Let:
- \( X \) = speed of Manoj in still water (in meters per second)
- \( Y \) = speed of the current (in meters per second)

### Step 3: Determine the effective speeds
When swimming upstream, Manoj's effective speed is \( X - Y \) (since he is swimming against the current). When swimming downstream, his effective speed is \( X + Y \) (since he is swimming with the current).

### Step 4: Calculate the distance covered in both directions
1. **Upstream:**
- Distance = Speed × Time
- Distance covered upstream in 12 seconds = \( (X - Y) \times 12 \)

2. **Downstream:**
- Distance covered downstream in 12 seconds = \( (X + Y) \times 12 \)

### Step 5: Set up the equation
According to the problem, the distance covered upstream plus the distance covered downstream equals the total distance between points P and Q, which is 144 meters. Therefore, we can set up the equation:
\[ (X - Y) \times 12 + (X + Y) \times 12 = 144 \]

### Step 6: Simplify the equation
Expanding the equation gives:
\[ 12X - 12Y + 12X + 12Y = 144 \]
Combining like terms:
\[ 24X = 144 \]

### Step 7: Solve for \( X \)
Dividing both sides by 24:
\[ X = \frac{144}{24} = 6 \text{ meters per second} \]

### Step 8: Find the speed of the current \( Y \)
Now, we need to find the speed of the current \( Y \). We can use the distances covered in each direction. Since the distance covered upstream is equal to the distance covered downstream, we can set the two equations for distance equal to each other:
\[ (X - Y) \times 12 = (X + Y) \times 12 - 144 \]

Substituting \( X = 6 \):
\[ (6 - Y) \times 12 = (6 + Y) \times 12 - 144 \]
Expanding both sides:
\[ 72 - 12Y = 72 + 12Y - 144 \]
Simplifying gives:
\[ 72 - 12Y = -72 + 12Y \]
Combining like terms:
\[ 144 = 24Y \]
Thus:
\[ Y = \frac{144}{24} = 6 \text{ meters per second} \]

### Conclusion
The speed of the current \( Y \) is **6 meters per second**.