Mohan takes 15 min to go to a market and 200 s to go to a bus stop travelling at the same speed. What is the ratio of distances in two cases?

Options

A. `4.5:1`
B. `5:1`
C. `1:4.5`
D. `4.5:6`

Answer

To find the ratio of distances that Mohan travels to the market and the bus stop, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Time taken to go to the market = 15 minutes
- Time taken to go to the bus stop = 200 seconds

2. **Convert Time to the Same Unit:**
- Convert 15 minutes into seconds:
\[ 15 \text{ minutes} = 15 \times 60 = 900 \text{ seconds} \]

3. **Define Speed:**
- Let the speed of Mohan be \( x \) (in meters per second).
- Speed is defined as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

4. **Set Up the Distance Equations:**
- For the market:
\[ \text{Distance to market} = x \times 900 \]
- For the bus stop:
\[ \text{Distance to bus stop} = x \times 200 \]

5. **Set Up the Ratio of Distances:**
- The ratio of distances can be expressed as:
\[ \frac{\text{Distance to market}}{\text{Distance to bus stop}} = \frac{x \times 900}{x \times 200} \]
- Since \( x \) is common in both distances, it cancels out:
\[ \frac{900}{200} \]

6. **Simplify the Ratio:**
- Simplifying \( \frac{900}{200} \):
\[ \frac{900 \div 100}{200 \div 100} = \frac{9}{2} \]

7. **Final Answer:**
- The ratio of distances to the market and the bus stop is:
\[ \text{Ratio} = 9 : 2 \]