A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speeds is:

Options

A. 3:4
B. 4:3
C. 3:5
D. 50 : 3

Answer

To find the ratio of the speeds of the truck and the bus, we will follow these steps:

### Step 1: Calculate the speed of the truck
The speed of the truck can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
The truck covers a distance of 550 meters in 1 minute. Thus, the speed of the truck is:
\[ \text{Speed of truck} = \frac{550 \text{ meters}}{1 \text{ minute}} = 550 \text{ meters per minute} \]

### Step 2: Convert the distance covered by the bus into meters
The bus covers a distance of 33 kilometers in 45 minutes. We need to convert kilometers to meters:
\[ 33 \text{ km} = 33 \times 1000 \text{ meters} = 33000 \text{ meters} \]

### Step 3: Calculate the speed of the bus
Now, we can calculate the speed of the bus using the same formula:
\[ \text{Speed of bus} = \frac{33000 \text{ meters}}{45 \text{ minutes}} \]
Calculating this gives:
\[ \text{Speed of bus} = \frac{33000}{45} = 733.33 \text{ meters per minute} \]

### Step 4: Find the ratio of the speeds
Now, we can find the ratio of the speeds of the truck to the bus:
\[ \text{Ratio of speeds} = \frac{\text{Speed of truck}}{\text{Speed of bus}} = \frac{550}{733.33} \]

### Step 5: Simplify the ratio
To simplify the ratio, we can multiply both the numerator and the denominator by 3 to eliminate the decimal:
\[ \text{Ratio} = \frac{550 \times 3}{733.33 \times 3} = \frac{1650}{2200} \]
Now, we can simplify this ratio:
\[ \text{Ratio} = \frac{1650 \div 110}{2200 \div 110} = \frac{15}{20} = \frac{3}{4} \]

### Final Answer
Thus, the ratio of the speeds of the truck to the bus is:
\[ \text{Ratio} = 3:4 \]

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