A car covers its journey at the speed of 40 km/hr in 8 hours. If the same distance is to be covered in 5 hours, by how much the speed of car will have to increase?

The correct option is 24 km/hr.

To find by how much the speed of the car needs to increase, we can break the problem down into three simple steps:
1. Calculate the total distance of the journey using the initial speed and time.
2. Determine the new speed required to cover this same distance in the new target time.
3. Find the difference between the new speed and the initial speed.

Step 1: Calculate the total distance
We are given that the car covers the journey at a speed of 40 km/hr in 8 hours. The formula relating distance, speed, and time is:

$\mathrm{Distance}=\mathrm{Speed}\times \mathrm{Time}$

Substituting the given values:

$\mathrm{Distance}=40\text{km/hr}\times 8\text{hours}=320\text{km}$

So, the total distance of the journey is 320 km.

Step 2: Calculate the new speed required
Now, we want to cover this same distance of 320 km in 5 hours. We can calculate the required new speed using the formula:

$\mathrm{New\; Speed}=\frac{\mathrm{Distance}}{\mathrm{New\; Time}}$

Substituting the values:

$\mathrm{New\; Speed}=\frac{320\text{km}}{5\text{hours}}=64\text{km/hr}$

The car must travel at a speed of 64 km/hr to finish the journey in 5 hours.

Step 3: Calculate the required increase in speed
To find out how much the speed needs to be increased, we subtract the initial speed from the new speed:

$\mathrm{Increase\; in\; Speed}=\mathrm{New\; Speed}-\mathrm{Initial\; Speed}$

$\mathrm{Increase\; in\; Speed}=64\text{km/hr}-40\text{km/hr}=24\text{km/hr}$

Therefore, the speed of the car must be increased by 24 km/hr.