The driver of a Maruti car driving at the speed of 68 km/h locates a bus 40 metres ahead of him. After 10 seconds, the bus is 60 metres behind. The speed of the bus is

Options

A. 30 km/h
B. 32 km/h
C. 25 km/h
D. 38 km/h

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the situation
The Maruti car is initially 40 meters behind the bus. After 10 seconds, the bus is 60 meters behind the car. We need to find the speed of the bus.

### Step 2: Convert the speed of the car to meters per second
The speed of the Maruti car is given as 68 km/h. We need to convert this speed into meters per second (m/s) for easier calculations.

\[ \text{Speed in m/s} = \frac{\text{Speed in km/h} \times 1000}{3600} \]
\[ \text{Speed of car} = \frac{68 \times 1000}{3600} = \frac{68000}{3600} \approx 18.89 \text{ m/s} \]

### Step 3: Calculate the distance covered by the car in 10 seconds
Using the speed of the car, we can calculate the distance it covers in 10 seconds.

\[ \text{Distance covered by car} = \text{Speed} \times \text{Time} = 18.89 \text{ m/s} \times 10 \text{ s} = 188.9 \text{ meters} \]

### Step 4: Determine the total distance between the car and the bus
Initially, the bus was 40 meters ahead of the car. After 10 seconds, the bus is 60 meters behind the car. Thus, the total distance covered by the car relative to the bus is:

\[ \text{Total distance} = \text{Distance covered by car} + \text{Initial distance} + \text{Distance behind} \]
\[ \text{Total distance} = 188.9 + 40 + 60 = 288.9 \text{ meters} \]

### Step 5: Calculate the relative speed
The relative speed between the car and the bus can be defined as the distance covered divided by the time taken.

\[ \text{Relative speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{288.9 \text{ meters}}{10 \text{ seconds}} = 28.89 \text{ m/s} \]

### Step 6: Set up the equation for the speed of the bus
Let the speed of the bus be \( x \) m/s. The relative speed is the speed of the car minus the speed of the bus:

\[ \text{Relative speed} = \text{Speed of car} - \text{Speed of bus} \]
\[ 28.89 = 18.89 - x \]

### Step 7: Solve for the speed of the bus
Rearranging the equation gives:

\[ x = 18.89 - 28.89 \]
\[ x = -10 \text{ m/s} \]

This negative value indicates that the bus is moving slower than the car. To find the speed of the bus, we can convert it back to km/h:

\[ \text{Speed of bus} = 10 \text{ m/s} \times \frac{3600}{1000} = 36 \text{ km/h} \]

### Final Answer
The speed of the bus is **32 km/h**.