P and Q starting simultaneously from two different places proceed towards each other at a speed of 20 km/hour and 30 km/hour respectively. By the time they meet each other. Q has covered 36km more than that of P. The distance (in km) between the two places is

Options

A. 144
B. 162
C. 180
D. 108

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the variables
Let:
- Speed of P = 20 km/h
- Speed of Q = 30 km/h
- Time taken to meet = T hours
- Distance covered by P = Distance covered by Q - 36 km

### Step 2: Write the equations for distances
The distance covered by P can be expressed as:
\[ \text{Distance covered by P} = 20 \times T \]

The distance covered by Q can be expressed as:
\[ \text{Distance covered by Q} = 30 \times T \]

### Step 3: Set up the equation based on the problem statement
According to the problem, Q has covered 36 km more than P:
\[ 30T = 20T + 36 \]

### Step 4: Solve the equation for T
Rearranging the equation:
\[ 30T - 20T = 36 \]
\[ 10T = 36 \]
\[ T = \frac{36}{10} = 3.6 \text{ hours} \]

### Step 5: Calculate the total distance between P and Q
The total distance between the two places is the sum of the distances covered by P and Q:
\[ \text{Total Distance} = \text{Distance covered by P} + \text{Distance covered by Q} \]
\[ \text{Total Distance} = 20T + 30T = 50T \]
Substituting T:
\[ \text{Total Distance} = 50 \times 3.6 = 180 \text{ km} \]

### Final Answer
The distance between the two places is **180 km**.

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