A car reached Raipur from Sonagarh in 35 min with an average speed of 69 km/h. If the average speed is increased by 36 km/h, how long will it take to cover the same distance?

Options

A. 24 min
B. 27 min
C. 23 min
D. 29 min

Answer

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

### Step 1: Convert the time from minutes to hours
The car took 35 minutes to travel from Sonagarh to Raipur. We need to convert this time into hours because the speed is given in km/h.

\[ \text{Time in hours} = \frac{35 \text{ minutes}}{60} = \frac{35}{60} = \frac{7}{12} \text{ hours} \]

### Step 2: Calculate the distance traveled
We can use the formula for distance, which is:

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

Given that the average speed is 69 km/h, we can calculate the distance:

\[ \text{Distance} = 69 \text{ km/h} \times \frac{7}{12} \text{ hours} = \frac{69 \times 7}{12} = \frac{483}{12} = 40.25 \text{ km} \]

### Step 3: Determine the new speed
The problem states that the average speed is increased by 36 km/h. Therefore, the new speed will be:

\[ \text{New Speed} = 69 \text{ km/h} + 36 \text{ km/h} = 105 \text{ km/h} \]

### Step 4: Calculate the time taken at the new speed
Now we will calculate the time taken to cover the same distance (40.25 km) at the new speed (105 km/h). We will use the formula:

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

Substituting the values we have:

\[ \text{Time} = \frac{40.25 \text{ km}}{105 \text{ km/h}} = \frac{40.25}{105} \text{ hours} \]

Calculating this gives:

\[ \text{Time} = \frac{40.25}{105} \approx 0.3833 \text{ hours} \]

### Step 5: Convert the time back to minutes
To convert the time back to minutes, we multiply by 60:

\[ \text{Time in minutes} = 0.3833 \text{ hours} \times 60 \approx 23 \text{ minutes} \]

### Final Answer
The time taken to cover the same distance at the increased speed is approximately **23 minutes**.

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