Aman goes to his office by car at the speed of 80 km/hr and reaches 10 minutes earlier. If he goes at the speed 30 km/hr, then he reaches 10 minutes late. What will be the speed of the car to reach on time?

Speed when Aman reaches 10 minutes earlier: 80 km/hr

Speed when Aman reaches 10 minutes late: 30 km/hr

Time difference between early and late arrival: 20 minutes (10 minutes early + 10 minutes late)

Speed = $$\frac{Distance}{Time}$$​​

For reaching earlier and late from original time:

Distance = $$\frac{\text{Increased speed} \times\text{Decreased speed}}{\text{Difference between speeds}}\times \frac{\text{ difference between early and late arrival }}{60}$$​​

Distance = $$\frac{80 \times 30}{50}\times \frac{20}{60}$$​ = 16 km

Now, For original time;

= $$\frac{16}{80} + \frac{10}{60} = \frac{1}{5}+ \frac{1}{6} = \frac{11}{30}$$​ hours

So, Original Speed :

= $$\frac{16}{\frac{11}{30}} = \frac{16 \times 30}{11} = \bf{ \frac{480}{11}}$$​ km/h