Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after traveling for one hour. If both cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?

The correct option is 15.

To find the duration for which car Q stopped, we first calculate the total time elapsed from the start of the journey to the final observation time.
The cars start at 10:00 AM and are observed at 11:30 AM.
Total time elapsed = 11:30 AM - 10:00 AM = 1.5 hours.

Car P travels continuously towards the North at a speed of 25 km/h for the entire duration of 1.5 hours.
The distance of car P from the starting point X is given by the formula:
Distance = Speed × Time
Substituting the values:

${\mathrm{Distance}}_P=25\times 1.5=37.5\text{km}$

Thus, at 11:30 AM, car P is 37.5 km away from point X.

We are given that both cars are at the same distance from X at 11:30 AM. Therefore, car Q is also at a distance of 37.5 km from X at that time.
Car Q travels East at a speed of 30 km/h. We can find the actual traveling time of car Q by dividing its distance by its speed:

${\mathrm{Time}}_Q=\frac{37.5\text{km}}{30\text{km/h}}=1.25\text{hours}$

Since the total elapsed time of the journey is 1.5 hours and car Q was actively moving for only 1.25 hours, the time that car Q remained stopped is calculated as follows:

$\mathrm{Stopping\; Time}=1.5-1.25=0.25\text{hours}$

To convert this duration into minutes, we multiply by 60:

$\mathrm{Stopping\; Time\; in\; Minutes}=0.25\times 60=15\text{minutes}$

Therefore, car Q stopped for 15 minutes.