RRB Technician Grade I 19 Dec 2024 Shift 3 Paper

Concept:When the angle of elevation of the sun increases, the shadow of a vertical pillar becomes shorter.The difference in shadow lengths helps us find the height of the pillar.Explanation:Let the height of the pillar be $h$ metres.For an angle of elevation $\theta$, the shadow length is given by $h \cot \theta$.So, the change in shadow length when the angle changes from $30^\circ$ to $45^\circ$ is:$$80 = h(\cot 30^\circ - \cot 45^\circ)$$Now, $\cot 30^\circ = \sqrt{3}$ and $\cot 45^\circ = 1$.Therefore:$$80 = h(\sqrt{3} - 1)$$Rearrange to find $h$:$$h = \frac{80}{\sqrt{3} - 1}$$Rationalise the denominator by multiplying numerator and denominator by $\sqrt{3} + 1$:$$h = \frac{80(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}$$$$h = \frac{80(\sqrt{3} + 1)}{3 - 1}$$$$h = \frac{80(\sqrt{3} + 1)}{2}$$$$h = 40(\sqrt{3} + 1) \text{ m}$$Answer:The height of the pillar is $40(\sqrt{3} + 1)$ m.So, the correct option is A.