Question

Radha travelled for 60 minutes. This travel of 60 minutes can be divided into 6 equal intervals of 10 minutes each. In these 6 intervals, she travelled 10 km, 12 km, 14 km, 9 km, 5 km and 15 km. What is the average speed of Radha if only those intervals are considered when her speed was between 50 km/hr and 80 km/hr?

• A. 62 km/hr
• B. 66 km/hr
• C. 58 km/hr
• D. 64.5 km/hr

Answer 1

The Correct Option is A

Average Speed Calculation 

- Radha's travel can be divided into 6 intervals of 10 minutes each. So, the total time for each interval is 10 minutes.

- To calculate the average speed when her speed is between 50 km/h and 80 km/h, we only consider the relevant intervals:

• 10 km: Speed = \( \frac{10}{10} \times 60 = 60 \text{ km/h} \) (✔ Between 50 km/h and 80 km/h)
• 12 km: Speed = \( \frac{12}{10} \times 60 = 72 \text{ km/h} \) (✔ Between 50 km/h and 80 km/h)
• 14 km: Speed = \( \frac{14}{10} \times 60 = 84 \text{ km/h} \) (❌ Greater than 80 km/h, not considered)
• 9 km: Speed = \( \frac{9}{10} \times 60 = 54 \text{ km/h} \) (✔ Between 50 km/h and 80 km/h)
• 5 km: Speed = \( \frac{5}{10} \times 60 = 30 \text{ km/h} \) (❌ Less than 50 km/h, not considered)
• 15 km: Speed = \( \frac{15}{10} \times 60 = 90 \text{ km/h} \) (❌ Greater than 80 km/h, not considered)

- The total distance travelled when her speed was between 50 km/h and 80 km/h is:

\[ 10 \text{ km} + 12 \text{ km} + 9 \text{ km} = 31 \text{ km} \]

- The total time taken for these 3 intervals is:

\[ 10 \text{ minutes} + 10 \text{ minutes} + 10 \text{ minutes} = 30 \text{ minutes} \]

- The average speed is calculated as follows:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \times 60 \] \[ \text{Average Speed} = \frac{31}{30} \times 60 = 62 \text{ km/h} \]

Thus, the average speed of Radha is 62 km/h.

Conclusion: The correct answer is (a) 62 km/h.