A bus started its journey from Ramgarh and reached Devgarh in 44 minutes with its average speed of 50km/hour. If the average speed of the bus is increased by 5km/hour, how much times will it take to cover the same distance ?

Options

A. 40 minutes
B. 38 minutes
C. 36 minutes
D. 31 minutes

Answer

To solve the problem step by step, we will use the formula for distance, which is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 1: Calculate the Distance
The bus travels from Ramgarh to Devgarh in 44 minutes at an average speed of 50 km/h. First, we need to convert the time from minutes to hours.

\[ \text{Time in hours} = \frac{44 \text{ minutes}}{60} = \frac{44}{60} = \frac{11}{15} \text{ hours} \]

Now, we can calculate the distance:

\[ \text{Distance} = \text{Speed} \times \text{Time} = 50 \text{ km/h} \times \frac{11}{15} \text{ hours} \]

Calculating this gives:

\[ \text{Distance} = \frac{50 \times 11}{15} = \frac{550}{15} \text{ km} = \frac{110}{3} \text{ km} \approx 36.67 \text{ km} \]

### Step 2: Calculate the New Time with Increased Speed
Now, if the average speed is increased by 5 km/h, the new speed becomes:

\[ \text{New Speed} = 50 \text{ km/h} + 5 \text{ km/h} = 55 \text{ km/h} \]

Now, we will use the same distance to find the new time taken to cover this distance at the new speed.

Using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:

\[ \text{Time} = \frac{\frac{110}{3} \text{ km}}{55 \text{ km/h}} = \frac{110}{3} \times \frac{1}{55} \]

Calculating this gives:

\[ \text{Time} = \frac{110}{165} = \frac{2}{3} \text{ hours} \]

### Step 3: Convert Time to Minutes
Finally, we convert the time from hours to minutes:

\[ \text{Time in minutes} = \frac{2}{3} \text{ hours} \times 60 \text{ minutes/hour} = 40 \text{ minutes} \]

### Conclusion
Thus, the time taken to cover the same distance at the increased speed of 55 km/h is **40 minutes**.

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