Indian Institute of Foreign Trade 2008 Solved Paper

Let us construct a diagram based on the given statements.
There are 2 diametrically opposite gates A and B.
A pole is erected on the circumference such that the distance of the pole from one of the gates is 7 m more than the distance of the pole from the other gate.
Let the distances be x and x+7 m.Now, APB is a right-angled triangle (since AB is the diameter).
Applying Pythagoras theorem, we get,
132=x2+(x+7)2
169=x2+x2+14x+49
120=2x2+14x
x2+7x−60=0
(x+12)(x−5)=0
Therefore, x can be -12 or 5
x cannot be negative. Therefore, x has to be 5.
The distance of the pole from one of the gates is 5 m. Therefore, option C is the right answer.