A bus starts running with the initial speed of 33 km/hr and its speed increases every hour by certain amount. If it takes 7 hours to cover a distance of 315 km, then what will be hourly increment (in km/hr) in the speed of the bus?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step-by-step, we can use the formula for the distance covered under uniform acceleration. The formula for the distance \( S \) covered in \( N \) hours with an initial speed \( A \) and a constant increment \( D \) in speed every hour is given by:

\[ S = \frac{N}{2} \times (2A + (N-1)D) \]

Where:
- \( S \) is the total distance covered,
- \( N \) is the total time in hours,
- \( A \) is the initial speed,
- \( D \) is the hourly increment in speed.

### Step 1: Identify the given values
From the problem:
- Initial speed \( A = 33 \) km/hr
- Total distance \( S = 315 \) km
- Total time \( N = 7 \) hours

### Step 2: Substitute the values into the formula
Using the formula:

\[ 315 = \frac{7}{2} \times (2 \times 33 + (7-1)D) \]

### Step 3: Simplify the equation
First, calculate \( 2 \times 33 \):

\[ 2 \times 33 = 66 \]

Now substitute back into the equation:

\[ 315 = \frac{7}{2} \times (66 + 6D) \]

### Step 4: Multiply both sides by 2 to eliminate the fraction
\[ 630 = 7 \times (66 + 6D) \]

### Step 5: Divide both sides by 7
\[ 90 = 66 + 6D \]

### Step 6: Isolate \( 6D \)
Subtract 66 from both sides:

\[ 90 - 66 = 6D \]
\[ 24 = 6D \]

### Step 7: Solve for \( D \)
Divide both sides by 6:

\[ D = \frac{24}{6} = 4 \]

### Conclusion
The hourly increment in the speed of the bus is \( 4 \) km/hr.