A vertical toy that is 18 cm high casts a shadow 8 cm long on the ground. At the same time and under the same lighting conditions, a vertical pole casts a shadow 48 m long on the ground. What is the height of the pole?

Introduction:
This question involves the concept of similar triangles formed by objects and their shadows when illuminated by the same light source, such as the sun. It is a standard height-and-distance problem used in aptitude exams to test proportional reasoning.

Given Data / Assumptions:

• Height of the toy = 18 cm.
• Length of the toy's shadow = 8 cm.
• Length of the pole's shadow = 48 m.
• Both toy and pole are vertical and illuminated under the same conditions, so the angles of elevation of the light source are equal.
• We must find the height of the pole.

Concept / Approach:
When two vertical objects cast shadows under the same lighting, the triangles formed by each object and its shadow are similar. For similar triangles, the ratio of corresponding sides (height to shadow) is equal.
Height of toy / Shadow of toy = Height of pole / Shadow of poleWe must also handle unit consistency, converting all measurements to the same unit if needed.

Step-by-Step Solution:
Step 1: Write the proportional relationship.18 cm / 8 cm = Height of pole / 48 mStep 2: Use the ratio 18 / 8.18 / 8 = 9 / 4Step 3: Express height of pole in metres.Height of pole = (18 / 8) * 48 mStep 4: Simplify stepwise.(18 / 8) * 48 = (9 / 4) * 48(9 / 4) * 48 = 9 * 12 = 108Therefore, height of pole = 108 m

Verification / Alternative check:
The height to shadow ratio for the toy is 18 : 8 which simplifies to 9 : 4. For the pole, with height 108 m and shadow 48 m, the ratio is 108 : 48, which simplifies by dividing both numbers by 12: 108 ÷ 12 = 9 and 48 ÷ 12 = 4. So the ratio is also 9 : 4, confirming similarity and correctness.

Why Other Options Are Wrong:
1080 cm (10.8 m): This does not preserve the correct ratio with the shadow length 48 m.
180 m and 96 m: These values give a different height-to-shadow ratio than 9 : 4, so they are inconsistent with similar triangles.
118 cm: This is far too small relative to a 48 m shadow and does not fit the proportion at all.

Common Pitfalls:
Students often mix up units (centimetres and metres) or forget to convert properly. Another mistake is using an incorrect ratio such as shadow/height instead of height/shadow. Staying consistent with ratios and units avoids these issues.

Final Answer:
The height of the pole is 108 m.