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

Answer

To find the ratio of the speeds of the truck and the bus, we will first calculate their individual speeds and then find the ratio.

### Step 1: Calculate the speed of the truck
The truck covers a distance of 550 meters in 1 minute.

1. Convert the distance from meters to kilometers:
\[ 550 \text{ meters} = \frac{550}{1000} \text{ kilometers} = 0.55 \text{ kilometers} \]

2. Convert the time from minutes to hours:
\[ 1 \text{ minute} = \frac{1}{60} \text{ hours} \]

3. Now, calculate the speed of the truck in kilometers per hour (km/h):
\[ \text{Speed of truck} = \frac{\text{Distance}}{\text{Time}} = \frac{0.55 \text{ km}}{\frac{1}{60} \text{ hours}} = 0.55 \times 60 = 33 \text{ km/h} \]

### Step 2: Calculate the speed of the bus
The bus covers a distance of 33 kilometers in 45 minutes.

1. Convert the time from minutes to hours:
\[ 45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours} \]

2. Now, calculate the speed of the bus in kilometers per hour (km/h):
\[ \text{Speed of bus} = \frac{\text{Distance}}{\text{Time}} = \frac{33 \text{ km}}{0.75 \text{ hours}} = 44 \text{ km/h} \]

### Step 3: Calculate the ratio of their speeds
Now that we have both speeds, we can find the ratio of the speed of the truck to the speed of the bus:
\[ \text{Ratio of speeds} = \frac{\text{Speed of truck}}{\text{Speed of bus}} = \frac{33 \text{ km/h}}{44 \text{ km/h}} = \frac{33}{44} = \frac{3}{4} \]

### Final Answer
The ratio of the speeds of the truck to the bus is \( \frac{3}{4} \).

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