Given Information:
- The aeroplane left 50 minutes later than its scheduled time.
- The distance to the destination is 1250 km.
- The aeroplane had to increase its speed by 250 km/hr from its usual speed to reach the destination in time.

To Find:
The usual speed of the aeroplane.

Explanation:

Step 1: Convert the Delay Time to Hours
The aeroplane left 50 minutes later than its scheduled time. To calculate the delay in hours, we need to convert 50 minutes to hours.

1 hour = 60 minutes

50 minutes = 50/60 hours = 5/6 hours

Step 2: Calculate the Time Taken
To calculate the time taken by the aeroplane to reach the destination, we need to consider the delay time and the increased speed.

Let the usual speed of the aeroplane be x km/hr.

The time taken at the usual speed = Distance / Speed = 1250 / x hours

The time taken with the increased speed = Distance / (x + 250) hours

Since the aeroplane left 50 minutes later, the time taken with the increased speed is (1250 / (x + 250)) - (5/6) hours.

Step 3: Equate the Time Taken
As the aeroplane had to reach the destination in time, the time taken at the usual speed and the time taken with the increased speed should be the same.

1250 / x = (1250 / (x + 250)) - (5/6)

Step 4: Solve the Equation
Let's solve the equation to find the usual speed of the aeroplane.

Multiply through by 6x(x + 250) to eliminate the fractions:

6 * 1250(x + 250) = 1250 * 6x - 5x(x + 250)

7500x + 6 * 1250 * 250 = 7500x - 5x^2 - 1250 * 5x

7500x + 1875000 = 7500x - 5x^2 - 6250x

Rearrange the equation to form a quadratic equation:

5x^2 - 6250x + 1875000 = 0

Solve the quadratic equation to find the value of x, which represents the usual speed of the aeroplane.

Step 5: Calculate the Usual Speed
Solving the quadratic equation, we find that x = 250 km/hr or x = 750 km/hr.

Since the aeroplane had to increase its speed by 250 km/hr, the usual speed cannot be 750 km/hr. Therefore, the usual speed of the aeroplane is 250 km/hr.

Answer:
The usual speed of the aeroplane is 250 km/hr.