A man walks `a` km in `b` hours. The time taken to walk 200 metres is

Options

A. `(200b)/(a)` hours
B. `(b)/(5a)` hours
C. `(b)/(a)` hours
D. `(ab)/(200)` hours

Answer

To find the time taken to walk 200 meters when a man walks `a` km in `b` hours, we can follow these steps:

### Step 1: Convert the distance from meters to kilometers
Since the man walks `a` km, we need to convert 200 meters into kilometers.
- 200 meters = 200/1000 km = 0.2 km

### Step 2: Calculate the speed of the man
The speed (S) of the man can be calculated using the formula:
\[ S = \frac{\text{Distance}}{\text{Time}} \]
Here, the distance is `a` km and the time is `b` hours. Therefore,
\[ S = \frac{a}{b} \text{ km/h} \]

### Step 3: Use the speed to find the time taken to walk 0.2 km
We can use the formula for time (T):
\[ T = \frac{\text{Distance}}{\text{Speed}} \]
Now, we need to find the time taken to walk 0.2 km:
\[ T = \frac{0.2 \text{ km}}{S} \]
Substituting the speed we found in Step 2:
\[ T = \frac{0.2}{\frac{a}{b}} \]

### Step 4: Simplify the expression
To simplify the expression:
\[ T = 0.2 \cdot \frac{b}{a} \]
\[ T = \frac{0.2b}{a} \]

### Step 5: Convert 0.2 into a fraction
We can express 0.2 as a fraction:
\[ 0.2 = \frac{2}{10} = \frac{1}{5} \]
Thus, we can rewrite the time as:
\[ T = \frac{1}{5} \cdot \frac{b}{a} \]
\[ T = \frac{b}{5a} \]

### Final Answer
The time taken to walk 200 meters is:
\[ \frac{b}{5a} \text{ hours} \]

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