Q57 / 90 · JEE Main 2016 (03 Apr) · Mathematics

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

  • A
    20
  • Correct answer
    B
    5
  • C
    6
  • D
    10

Solution

Figure

ΔQPA :hx+y=tan30°

⇒3h=x+y ......i

ΔQPB :hy=tan60°

⇒h= 3y   ......ii

From equation i & ii, we get

3y=x+y 

⇒y=x2

∵ Speed is uniform

Therefore, distance x walked by him in 10 min.

and distance x2 walked by him in 5 min.

Hence, the correct answer is option: 'B'.

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