A train runs at a speed of 84 kmph to cover a distance of 336 km and then at a speed of 96 kmph to cover a distance of 192 km. Find the average speed of the train for the entire distance.

Correct option is C

Given:
First segment: Speed = 84 km/h, Distance = 336 km

Second segment: Speed = 96 km/h, Distance = 192 km

Formula Used:

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

Solution:

Total Distance = 336 km + 192 km = 528 km 

​​$$\text{Time}_1 = \frac{\text{Distance}_1}{\text{Speed}_1} = \frac{336\,\text{km}}{84\,\text{km/h}} = 4\,\text{hours}$$​

​$$\text{Time}_2 = \frac{\text{Distance}_2}{\text{Speed}_2} = \frac{192\,\text{km}}{96\,\text{km/h}} = 2\,\text{hours}$$  

​$$\text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4\,\text{hours} + 2\,\text{hours} = 6\,\text{hours}$$ 

​$$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{528\,\text{km}}{6\,\text{hours}} = 88\,\text{km/h}$$ 

Option (c) is right.