Question

A man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2. The height of man is 2 m. It is noticed that shadow of the man with respect to first lamp post just touches the foot of second lamp post. If the distance between the posts is 30 m, find the height of the first post.

• A. 6m
• B. 5 m
• C. 4m
• D. 3 m

Answer 1

The Correct Option is D

Let the height of the first lamp post be \( h_1 \), and the height of the second lamp post be \( h_2 \). The man divides the distance between the two posts in the ratio 1:2. The total distance between the posts is 30 m, so the distance between the man and the first lamp post is: \[ \frac{1}{3} \times 30 = 10 \, \text{m} \] The distance between the man and the second lamp post is: \[ \frac{2}{3} \times 30 = 20 \, \text{m} \] Now, we can apply similar triangles. The height of the first lamp post and the distance between the first lamp post and the man form a triangle, as does the height of the man and the distance between the man and the second lamp post. The ratio of the heights of the lamp post to the man is equal to the ratio of their respective distances. \[ \frac{h_1}{2} = \frac{10}{20} \] Solving for \( h_1 \): \[ h_1 = 2 \times \frac{10}{20} = 4 \, \text{m} \]

The correct option is (D): \(3\ m\)