Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. What is the average speed of the car?

The correct option is 48 km/hr.

To find the average speed of the car for the entire journey, we must use the fundamental definition of average speed:

$$\text{Average Speed}=\frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}$$

Let us break down the journey into two parts: going from city A to city B, and returning from city B to city A.
The distance between city A and city B is given as 360 km. Since the car returns back to the starting point, it travels the same distance on the way back.

Step 1: Calculate the total distance travelled
The car travels from A to B (360 km) and then from B to A (360 km).
Total Distance = 360 km + 360 km = 720 km

Step 2: Calculate the time taken for each leg of the journey
We use the formula: Time = Distance / Speed.

For the outward journey from A to B:
Distance = 360 km
Speed = 40 km/hr
Time taken (t₁) is: $$t_1=\frac{360\text{km}}{40\text{km/hr}}=9\text{hours}$$

For the return journey from B to A:
Distance = 360 km
Speed = 60 km/hr
Time taken (t₂) is: $$t_2=\frac{360\text{km}}{60\text{km/hr}}=6\text{hours}$$

Step 3: Calculate the total time taken
Total Time = t₁ + t₂ = 9 hours + 6 hours = 15 hours

Step 4: Calculate the average speed
Now, we substitute the total distance and total time into our average speed formula: $$\text{Average Speed}=\frac{720\text{km}}{15\text{hours}}=48\text{km/hr}$$

Alternatively, when a journey covers equal distances at two different speeds, say v₁ and v₂, the average speed can be calculated directly using the harmonic mean formula: $$\text{Average Speed}=\frac{2·v_1·v_2}{v_1+v_2}$$ Substituting v₁ = 40 km/hr and v₂ = 60 km/hr: $$\text{Average Speed}=\frac{2·40·60}{40+60}=\frac{4800}{100}=48\text{km/hr}$$