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EEJ MAIN Mathematics QUESTION #7465
Question 1
A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30°. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60°. Then the time taken (in minutes) by him, from B to reach the pillar, is:
  • 10
  • 20
  • 5✔️
  • 6
Correct Answer Explanation
Let the height of pillar be \(h\) and the man's speed be \(v\). Let distances from pillar be \(d_A\) at A and \(d_B\) at B. From angles: \(\tan 30° = \frac{h}{d_A}\) gives \(d_A = h\sqrt{3}\), and \(\tan 60° = \frac{h}{d_B}\) gives \(d_B = \frac{h}{\sqrt{3}}\). Distance AB = \(d_A - d_B = h\sqrt{3} - \frac{h}{\sqrt{3}} = \frac{3h-h}{\sqrt{3}} = \frac{2h}{\sqrt{3}}\). Time for AB is 10 minutes, so \(v = \frac{2h}{\sqrt{3} \cdot 10} = \frac{h}{5\sqrt{3}}\). Time from B to pillar = \(\frac{d_B}{v} = \frac{h/\sqrt{3}}{h/(5\sqrt{3})} = 5\) minutes.