A bus goes from Jaipur to Delhi with a speed of 30 Kmph and comes back with a speed of 60 Kmph. What will be the average speed of the bus (in Kmph)?

Question

Accepted Answer

**The correct option is 1 (40 Kmph):****Detailed Explanation**

The question asks for the average speed of a bus that travels an equal distance ($D$) from Jaipur to Delhi at speed $v\_1 = 30 \text{ Kmph}$ and returns the same distance from Delhi to Jaipur at speed $v\_2 = 60 \text{ Kmph}$. When an object covers the *same distance* at two different speeds, the average speed is calculated using the formula for the harmonic mean of the two speeds, not the simple arithmetic mean.

The formula for average speed in this specific scenario is:
$$\text{Average Speed} = \frac{2 \times v\_1 \times v\_2}{v\_1 + v\_2}$$

Plugging in the given values:
$$\text{Average Speed} = \frac{2 \times 30 \text{ Kmph} \times 60 \text{ Kmph}}{30 \text{ Kmph} + 60 \text{ Kmph}} = \frac{3600}{90} \text{ Kmph} = 40 \text{ Kmph}$$

This formula ensures that the calculation correctly accounts for the *time* spent on each leg of the journey, which is longer for the slower speed (30 Kmph) and shorter for the faster speed (60 Kmph). Since the bus spends more time traveling at the slower speed, the average speed must be closer to 30 Kmph than to 60 Kmph. Therefore, the average speed is 40 Kmph, which is correctly represented by Option 1.-----**Incorrect Options**

**The incorrect option is 2 (30 Kmph):**
This value is the speed of the bus only for the first leg of the journey. The bus also travels at a higher speed (60 Kmph) for the return journey, which must raise the overall average speed. This answer would only be correct if the bus had traveled the entire distance at 30 Kmph.

**The incorrect option is 3 (50 Kmph):**
This value represents the simple arithmetic mean of the two speeds: $\frac{30 + 60}{2} = 45 \text{ Kmph}$. However, the arithmetic mean is only the correct average speed if the bus had traveled for an *equal amount of time* at each speed, not an equal distance. Since the distance is the same, the time spent at 30 Kmph is double the time spent at 60 Kmph, pulling the true average down from 45 Kmph to 40 Kmph.

**The incorrect option is 4 (60 Kmph):**
This value is the speed of the bus only for the return leg of the journey. Since the bus also travels at a slower speed (30 Kmph), the average speed must be lower than 60 Kmph. This option does not account for the entire trip's duration, making it incorrect for the average speed.