The driver of an ambulance sees a school bus 40 m ahead of him after 20 sec the school bus is 60 metre behind.if the speed of ambulance is 30 km/h What is the speed of the school bus?

Options

A. 10 km/h
B. 12 km/h
C. 15km/h
D. 22 km/h

Answer

To solve the problem step by step, we will analyze the situation involving the ambulance and the school bus.

### Step 1: Understand the Initial Setup
- The ambulance driver sees the school bus 40 meters ahead of him.
- After 20 seconds, the school bus is 60 meters behind the ambulance.

### Step 2: Determine the Distance Covered
- Initially, the distance between the ambulance and the school bus is 40 meters.
- After 20 seconds, the distance between them changes to 60 meters behind the ambulance.
- Therefore, the total distance covered by the ambulance in relation to the school bus is:
\[ \text{Total distance} = 40 \text{ m} + 60 \text{ m} = 100 \text{ m} \]

### Step 3: Calculate the Speed of the Ambulance
- The speed of the ambulance is given as 30 km/h.
- To convert this speed into meters per second (m/s):
\[ \text{Speed of ambulance} = 30 \text{ km/h} = \frac{30 \times 1000}{3600} \text{ m/s} = \frac{30000}{3600} \text{ m/s} \approx 8.33 \text{ m/s} \]

### Step 4: Calculate the Distance Covered by the Ambulance in 20 Seconds
- Using the speed of the ambulance, we can calculate the distance it covers in 20 seconds:
\[ \text{Distance covered by ambulance} = \text{Speed} \times \text{Time} = 8.33 \text{ m/s} \times 20 \text{ s} = 166.67 \text{ m} \]

### Step 5: Determine the Relative Speed
- The distance covered by the ambulance is 166.67 m, but relative to the school bus, it is 100 m.
- Therefore, the distance covered by the school bus in the same time must be:
\[ \text{Distance covered by school bus} = \text{Distance covered by ambulance} - \text{Total distance} = 166.67 \text{ m} - 100 \text{ m} = 66.67 \text{ m} \]

### Step 6: Calculate the Speed of the School Bus
- Now, we can find the speed of the school bus:
\[ \text{Speed of school bus} = \frac{\text{Distance}}{\text{Time}} = \frac{66.67 \text{ m}}{20 \text{ s}} = 3.33 \text{ m/s} \]
- To convert this back to km/h:
\[ \text{Speed of school bus} = 3.33 \text{ m/s} \times \frac{3600}{1000} \approx 12 \text{ km/h} \]

### Final Answer
The speed of the school bus is approximately **12 km/h**.

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