Answer :
Let the original speed of the plane be x km/h
Actual speed of the plane = (x + 100) km/h
Distance of journey = 1500km
Time taken to reach destination at original speed = 
Time taken to reach destination at actual speed = 
According to given question
30 mins = 1/2 hr
x2 + 100x = 300000
x2 + 100x – 300000 = 0
Using the splitting middle term – the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1 b = 100 c = – 300000
= 1. – 300000 = – 300000
And either of their sum or difference = b
= 100
Thus the two terms are 600 and – 500
Difference = 600 – 500 = 100
Product = 600. – 500 = – 300000
x2 + 600x – 500x + 300000 = 0
x (x + 600) – 500(x + 600) = 0
(x + 600)(x – 500) = 0
x = – 600 or x = 500
x = 500 (speed cannot be negative)
Hence the original speed of the plane is 500 km/hr
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