An express train covers a fixed distance in 40 minutes at an average speed of 200 km/h. Due to construction work, it needs to be diverted, increasing the distance by 25%. If the train needs to arrive at its destination on time (in 40 minutes), what should its new average speed be in km/h?

The correct answer is 250 km/h.

Step 1: Calculate the original distance covered by the train.
We are given that the train covers a fixed distance in 40 minutes at an average speed of 200 km/h.
First, convert the time from minutes to hours:

$\text{Time}=\frac{40}{60}\text{hours}=\frac{2}{3}\text{hours}$

Now, using the formula $\text{Distance}=\text{Speed}\times \text{Time}$, we find the original distance:

$\text{Original Distance}=200\times \frac{2}{3}=\frac{400}{3}\text{km}$

Step 2: Calculate the new distance after diversion.
The distance is increased by 25% due to construction work.
Therefore, the new distance is 125% of the original distance:

$\text{New Distance}=\frac{400}{3}\times (1+\frac{25}{100})=\frac{400}{3}\times \frac{5}{4}=\frac{500}{3}\text{km}$

Step 3: Calculate the new required average speed.
The train still needs to reach the destination in the same time, which is 40 minutes ($\frac{2}{3}$ hours).
Using the formula $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$:

$\text{New Speed}=\frac{\frac{500}{3}}{\frac{2}{3}}=\frac{500}{3}\times \frac{3}{2}=250\text{km/h}$

Thus, the new average speed of the train must be 250 km/h to arrive on time.