A salesman travels a distance of 50 km in 2 hours and 30 minutes. How much faster, in kilometres per hour, on an average, must he travel to make such a trip in $\frac{5}{6}$ hour less time?

### Concept & Change in Speed Calculate the initial speed and the required new speed based on the altered time, then find the absolute difference between the two speeds. ### Step-by-Step Solution * **Initial Scenario:** Distance = 50 km. Time = 2 hours 30 mins = $2.5$ hours = $\frac{5}{2}$ hours. * Initial Speed = $\frac{50}{\frac{5}{2}} = 50 \times \frac{2}{5} = 20$ km/hr. * **New Scenario:** The new time should be $\frac{5}{6}$ hour less. * New Time = $\frac{5}{2} - \frac{5}{6} = \frac{15 - 5}{6} = \frac{10}{6} = \frac{5}{3}$ hours. * New Speed = $\frac{\text{Distance}}{\text{New Time}} = \frac{50}{\frac{5}{3}} = 50 \times \frac{3}{5} = 30$ km/hr. * **Difference:** Increase in speed = $30 - 20 = 10$ km/hr. ### Exam Strategy & Shortcut Initial time is 2.5 hrs (150 mins). $\frac{5}{6}$ of an hour is 50 mins. New time = 100 mins ($\frac{5}{3}$ hrs). Initial speed = $\frac{50}{2.5} = 20$. New speed = $\frac{50}{5/3} = 30$. The difference is $10$. Thinking purely in minutes for the time steps can sometimes prevent fraction addition errors. ### Common Pitfall Selecting the new speed (30) as the final answer instead of the *increase* in speed (10). Always re-read the final question prompt carefully to see exactly what is being asked. ### Final Answer Therefore, the correct answer is **10**.