R reaches office from home in 30 minutes and comes back in 20 minutes. The distance to his office from home is 12.5 km. What is his average speed (in km/h) from home to office and then back home?

The correct option is 30.

Step-by-Step Explanation:

To find the average speed of the entire journey (from home to office and back home), we use the formula for average speed:

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

Step 1: Calculate the Total Distance
The distance from home to the office is 12.5 km. Since R goes to the office and then returns home, the total distance traveled is:

$\text{Total Distance}=12.5\text{km}+12.5\text{km}=25\text{km}$

Step 2: Calculate the Total Time Taken
The time taken to reach the office is 30 minutes, and the time taken to return home is 20 minutes. The total time taken is:

$\text{Total Time}=30\text{minutes}+20\text{minutes}=50\text{minutes}$

Step 3: Convert the Total Time to Hours
Since the speed needs to be in kilometers per hour (km/h), we convert the total time from minutes to hours by dividing by 60:

$\text{Total Time (in hours)}=\frac{50}{60}\text{hours}=\frac{5}{6}\text{hours}$

Step 4: Calculate the Average Speed
Now, substitute the total distance and total time (in hours) into the average speed formula:

$\text{Average Speed}=\frac{25}{\left(\frac{5}{6}\right)}$

$\text{Average Speed}=25\times \frac{6}{5}$

$\text{Average Speed}=5\times 6=30\text{km/h}$

Thus, the average speed of R from home to office and back home is 30 km/h.