The ratio of speeds of two trains, one travelling at 45 km/hour and the other at 10 m/sec is -

Options

A. 5:4
B. 2 :3
C. 3 :4
D. 4:3

Answer

To find the ratio of the speeds of the two trains, we will follow these steps:

### Step 1: Identify the speeds of the trains
- The speed of the first train (V1) is given as 45 km/hour.
- The speed of the second train (V2) is given as 10 m/sec.

### Step 2: Convert the speed of the first train to m/sec
To compare the speeds, we need to convert the speed of the first train from km/hour to m/sec. The conversion factor is:
1 km/hour = (1000 meters / 3600 seconds) = 1/3.6 m/sec.

So, to convert 45 km/hour to m/sec:
\[ V1 = 45 \text{ km/hour} \times \frac{1}{3.6} \text{ m/sec} \]
Calculating this gives:
\[ V1 = 45 \div 3.6 = 12.5 \text{ m/sec} \]

### Step 3: Write down the speed of the second train
- The speed of the second train (V2) is already given as 10 m/sec.

### Step 4: Find the ratio of the speeds
Now we can find the ratio of the speeds of the two trains:
\[ \text{Ratio} = \frac{V1}{V2} = \frac{12.5 \text{ m/sec}}{10 \text{ m/sec}} \]
Calculating this gives:
\[ \text{Ratio} = \frac{12.5}{10} = 1.25 \]

### Step 5: Express the ratio in simplest form
To express the ratio in simplest form, we can write:
\[ 1.25 = \frac{5}{4} \]
Thus, the ratio of the speeds of the two trains is:
\[ \text{Ratio} = 5:4 \]

### Final Answer
The ratio of the speeds of the two trains is **5:4**.

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