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

Options

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

Answer

To solve the problem step by step, we will first find the distance traveled by the car and then calculate the time taken at the new speed.

### Step 1: Find the distance traveled by the car.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Average speed = 69 km/h
- Time = 35 minutes

First, we need to convert the time from minutes to hours:
\[ \text{Time in hours} = \frac{35 \text{ minutes}}{60} = \frac{35}{60} = \frac{7}{12} \text{ hours} \]

Now we can calculate the distance:
\[ \text{Distance} = 69 \text{ km/h} \times \frac{7}{12} \text{ hours} \]
\[ \text{Distance} = \frac{69 \times 7}{12} \]
\[ \text{Distance} = \frac{483}{12} \text{ km} \]
\[ \text{Distance} = 40.25 \text{ km} \]

### Step 2: Calculate the new speed.
The new speed is increased by 36 km/h:
\[ \text{New speed} = 69 \text{ km/h} + 36 \text{ km/h} = 105 \text{ km/h} \]

### Step 3: Find the time taken to cover the same distance at the new speed.
Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:
\[ \text{Time} = \frac{40.25 \text{ km}}{105 \text{ km/h}} \]

Calculating the time:
\[ \text{Time} = \frac{40.25}{105} \text{ hours} \]
\[ \text{Time} = \frac{40.25 \times 60}{105} \text{ minutes} \]
\[ \text{Time} = \frac{2415}{105} \text{ minutes} \]
\[ \text{Time} \approx 23 \text{ minutes} \]

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

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