A man walks a certain distance and takes total time of 37 min. When returning by vehicle. He can walk 55 min. both the sides. How much time will he take to travel by vehicle both sides ?

Options

A. 19 minute
B. 20 minute
C. 9.5 minute
D. 18 minute

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the problem
The man takes a total of 37 minutes to walk a certain distance and return by vehicle. When he walks both ways, it takes him 55 minutes.

### Step 2: Set up the equations
Let:
- \( W \) = time taken to walk one way
- \( R \) = time taken to ride one way

From the problem, we have two equations:
1. \( W + R = 37 \) (total time for walking one way and riding back)
2. \( 2W = 55 \) (total time for walking both ways)

### Step 3: Solve for \( W \)
From the second equation:
\[ 2W = 55 \]
Dividing both sides by 2:
\[ W = \frac{55}{2} = 27.5 \text{ minutes} \]

### Step 4: Substitute \( W \) into the first equation
Now, substitute \( W \) into the first equation:
\[ 27.5 + R = 37 \]
To find \( R \), subtract 27.5 from both sides:
\[ R = 37 - 27.5 = 9.5 \text{ minutes} \]

### Step 5: Calculate the total time for the vehicle both ways
Since the time taken to ride one way is \( R = 9.5 \) minutes, the time taken to ride both ways is:
\[ 2R = 2 \times 9.5 = 19 \text{ minutes} \]

### Final Answer
The man will take **19 minutes** to travel by vehicle both ways.

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