A motorist covers a distance of 30 km in 50 minutes by moving at a speed of x km/hr for the first 13 minutes, then moving at the speed of 2x km/hr for the next 25 minutes and then again moving at the speed of x km/hr for the rest of the journey. The value of x is equal to:​

Correct option is D

Given:
Total distance = 30 km
Total time = 50 minutes = $$\frac 56$$​ hours
Speed for the first 13 minutes = x km/hr
Speed for the next 25 minutes = 2x km/hr
Speed for the remaining part of the journey = x km/hr
Formula Used:
Distance = Speed × Time
Time taken for each part of the journey = Distance / Speed
Solution:
​$$13 \, \text{minutes} = \frac{13}{60} \, \text{hours}\\25 \, \text{minutes} = \frac{25}{60} \, \text{hours}\\\text{Remaining time} = \frac{50}{60} - \frac{13}{60} - \frac{25}{60} = \frac{12}{60} = \frac{1}{5} \, \text{hours}\\$$​​:
Distance traveled in the first 13 minutes = $$x \times \frac{13}{60} \, \text{km}$$​

Distance traveled in the next 25 minutes = $$2x \times \frac{25}{60} \, \text{km}$$​
Distance traveled in the remaining time = $$x \times \frac{1}{5} \, \text{km}$$​
Total distance =30 km
​$$x \times \frac{13}{60} + 2x \times \frac{25}{60} + x \times \frac{1}{5} = 30\\\Rightarrow \frac{63x}{60} + \frac{12x}{60} = 30\\\Rightarrow \frac{75x}{60} = 30\\\Rightarrow 75x = 30 \times 60\\\Rightarrow 75x = 1800\\\Rightarrow x = \frac{1800}{75} = 24 \text{km/hr}\\$$