A train travels at a speed of 40 km/hr and another train at a speed of 20 m/s. find ratio of speed of the first train to that of the second train ?

Options

A. `2:1`
B. ` 5 :9`
C. `5 :3`
D. `9 :5`

Explanation

To find the ratio of the speed of the first train to that of the second train, we will follow these steps:

### Step 1: Convert the speed of the second train from m/s to km/hr
The speed of the second train is given as 20 m/s. To convert this to km/hr, we can use the conversion factor:
1 m/s = 3.6 km/hr

So,
\[ \text{Speed of second train} = 20 \, \text{m/s} \times 3.6 \, \text{km/hr per m/s} = 72 \, \text{km/hr} \]

### Step 2: Write down the speed of the first train
The speed of the first train is already given as 40 km/hr.

### Step 3: Set up the ratio of the speeds
Now we need to find the ratio of the speed of the first train to the speed of the second train:
\[ \text{Ratio} = \frac{\text{Speed of first train}}{\text{Speed of second train}} = \frac{40 \, \text{km/hr}}{72 \, \text{km/hr}} \]

### Step 4: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by 8:
\[ \text{Ratio} = \frac{40 \div 8}{72 \div 8} = \frac{5}{9} \]

### Final Answer
The ratio of the speed of the first train to that of the second train is:
\[ \frac{5}{9} \]

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