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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 6.1 Introduction
If a vertical pole of length 7·5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is :
  1. A 20 m
  2. B 40 m
  3. C 60 m
  4. D 36 m
Previously asked in CBSE board exam
2024 30/5/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer

The correct answer is (D) 36 m.

Using similarity of triangles (AA criterion), the ratio of height to shadow length is constant:

$$\frac{7.5}{5} = \frac{h}{24} \Rightarrow h = \frac{7.5 \times 24}{5} = 36 \text{ m}$$

Explanation

At the same time of day, the sun's rays are parallel, so a vertical pole and a tower cast shadows that form equiangular (similar) triangles with the ground. This means height/shadow ratios are equal. Set up the proportion and solve for the unknown height. This is a direct application of the AA similarity criterion from Chapter 6.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.