A train runs at a speed of 92 kmph to cover a distance of 184 km and then at a speed of 102 kmph to cover a distance of 204km. Find the average speed of the train for the entire distance.

Correct option is D

Given:

Speed 1 = 92 kmph

Distance 1 = 184 km

Speed 2 = 102 kmph

Distance 2 = 204 km

Formula Used:

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

Time = $$\frac{\text{Distance}}{\text{Speed}}$$​​

Solution:

Time 1 = $$\frac{\text{Distance}_1}{\text{Speed}_1} = \frac{184 \, \text{km}}{92 \, \text{km/h}} = 2 \, \text{hours}$$​​

Time 2 = $$\frac{\text{Distance}_2}{\text{Speed}_2} = \frac{204 \, \text{km}}{102 \, \text{km/h}} = 2 \, \text{hours}$$​​

Total Distance = Distance 1 + Distance 2 = 184 km + 204 km = 388 km

Total Time = Time 1 + Time 2 = 2 hours + 2 hours = 4 hours

Average Speed = $$\frac{\text{Total Distance}}{\text{Total Time}} = \frac{388 \, \text{km}}{4 \, \text{hours}} = 97 \, \text{km/h}$$​​

Therefore, the average speed of the train for the entire distance is 97 kmph.

Option (d) is right.