Ravi and Ajay start simultaneously from a place A towards B, 60 km apart. Ravi's speed is 4km/hr less than that of Ajay. Ajay, after reaching B, turns back and meets Ravi at a place 12km away from B. Ravi's speed is

Options

A. 12km/hr
B. 10km/hr
C. 8km/hr
D. 6km/hr

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the Variables
Let Ajay's speed be \( x + 4 \) km/hr. Therefore, Ravi's speed will be \( x \) km/hr (since Ravi's speed is 4 km/hr less than Ajay's).

**Hint:** Define the speeds of both individuals based on the information given in the question.

### Step 2: Understand the Distances
The distance between points A and B is 60 km. After reaching B, Ajay turns back and meets Ravi at a point that is 12 km away from B. This means that the distance Ravi has traveled when they meet is \( 60 - 12 = 48 \) km.

**Hint:** Visualize the problem to understand the distances traveled by both Ravi and Ajay.

### Step 3: Set Up the Time Equation
Since both Ravi and Ajay start at the same time, the time taken by both to reach the meeting point O is the same.

Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

For Ravi:
\[ \text{Time}_{Ravi} = \frac{48}{x} \]

For Ajay:
\[ \text{Time}_{Ajay} = \frac{72}{x + 4} \]
(Here, 72 km is the total distance Ajay traveled: 60 km to B and 12 km back to O).

**Hint:** Remember that the time taken by both Ravi and Ajay to meet is equal.

### Step 4: Set the Times Equal
Since the times are equal:
\[ \frac{48}{x} = \frac{72}{x + 4} \]

**Hint:** Set the two expressions for time equal to each other to form an equation.

### Step 5: Cross Multiply to Solve for x
Cross multiplying gives:
\[ 48(x + 4) = 72x \]

Expanding this:
\[ 48x + 192 = 72x \]

**Hint:** Use algebraic manipulation to simplify the equation.

### Step 6: Rearrange the Equation
Rearranging the equation gives:
\[ 192 = 72x - 48x \]
\[ 192 = 24x \]

**Hint:** Isolate the variable \( x \) to find its value.

### Step 7: Solve for x
Dividing both sides by 24:
\[ x = \frac{192}{24} = 8 \text{ km/hr} \]

**Hint:** Perform the division carefully to find the speed of Ravi.

### Step 8: Find Ravi's Speed
Since Ravi's speed is \( x \):
\[ \text{Ravi's speed} = 8 \text{ km/hr} \]

**Hint:** Substitute the value of \( x \) back to find Ravi's speed.

### Final Answer
Ravi's speed is **8 km/hr**.