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,
${13}^2={\mathit{x}}^2+{\left(\mathit{x}+7\right)}^2$
$169={\mathit{x}}^2+{\mathit{x}}^2+14\mathit{x}+49$
$120=2{\mathit{x}}^2+14\mathit{x}$
${\mathit{x}}^2+7\mathit{x}-60=0$
$\left(\mathit{x}+12\right)\left(\mathit{x}-5\right)=0$
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.