One morning Vaidehi cycled from her house to her office at $15\text{km/hr}$ but owing to heavy traffic could return from her office at $10\text{km/hr}$. What was the average speed for the two-way trip?

Let the speed from house to office be $x=15\text{km/hr}$ and the return speed be $y=10\text{km/hr}$.
Since the distance covered in both directions is the same, the average speed for the two-way trip is given by the harmonic mean formula:

$$\text{Average Speed}=\frac{2xy}{x+y}$$

Substitute the values into the formula:

$$\text{Average Speed}=\frac{2\times 15\times 10}{15+10}$$

$$\text{Average Speed}=\frac{300}{25}=12\text{km/hr}$$

Thus, the average speed for the two-way trip was $12\text{km/hr}$.