Manoj and Hemant starts their journey at the same time from A and B towards B and A with speed of 36km/h and 24 km/h respectively. After reaching their destination they retrace their path towards each other. Find distance cover by Manoj, if total distance between A and B is 25 km?

Options

A. A)30 km
B. B)45 km
C. C)48 km
D. D)50 km

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the speeds and the total distance
Manoj travels at a speed of 36 km/h and Hemant at 24 km/h. The total distance between points A and B is 25 km.

**Hint:** Identify the speeds of both travelers and the total distance they need to cover.

### Step 2: Calculate the ratio of their speeds
The ratio of Manoj's speed to Hemant's speed is:
\[ \text{Speed Ratio} = \frac{36}{24} = \frac{3}{2} \]

**Hint:** Simplify the speeds to find the ratio, which will help in determining the distances they travel.

### Step 3: Set up the distance ratio
Since they travel for the same amount of time until they meet, the distances they cover will be in the same ratio as their speeds. Let the distance traveled by Manoj be \(3x\) and the distance traveled by Hemant be \(2x\).

**Hint:** Use the speed ratio to express the distances in terms of a variable.

### Step 4: Write the equation for total distance
The total distance covered by both Manoj and Hemant when they meet is equal to the distance between A and B:
\[ 3x + 2x = 25 \text{ km} \]
\[ 5x = 25 \]

**Hint:** Combine the distances to form an equation that equals the total distance.

### Step 5: Solve for \(x\)
Dividing both sides by 5 gives:
\[ x = 5 \]

**Hint:** Isolate the variable to find its value.

### Step 6: Calculate the distance covered by Manoj
Now, substituting \(x\) back into the distance for Manoj:
\[ \text{Distance covered by Manoj} = 3x = 3 \times 5 = 15 \text{ km} \]

**Hint:** Substitute the value of \(x\) back into the expression for Manoj's distance.

### Step 7: Calculate the distance covered after retracing
After reaching their destinations, they retrace their paths towards each other. The distance they cover while retracing is the same as the distance they initially traveled. Thus, the total distance covered by Manoj is:
\[ \text{Total distance covered by Manoj} = 15 \text{ km} (to B) + 15 \text{ km} (back to meet Hemant) = 30 \text{ km} \]

**Hint:** Remember that the distance covered while retracing is equal to the distance initially traveled.

### Final Answer
The total distance covered by Manoj is **30 km**.