In an old palace there are 50 stairs to reach the top floor. Each stair is 20 cm high, 30 cm wide, and 60 cm long. If all the stairs are re-plastered at the rate of Rs 4 per 100 sq cm (plastering the tread and riser surfaces), what is the total expenditure?

Introduction / Context:
This is a surface area and cost problem involving repeated identical objects (stairs). For re-plastering steps, the commonly plastered exposed faces are the top horizontal surface (tread) and the front vertical surface (riser). Using the given dimensions, we compute the area of these faces for one stair in square centimetres, multiply by the number of stairs to get total plaster area, then apply the rate given per 100 sq cm. The main skill is careful area calculation with consistent units, and applying the rate correctly by grouping the total area into blocks of 100 sq cm.

Given Data / Assumptions:

• Number of stairs = 50
• Height (riser) = 20 cm
• Width = 30 cm
• Length = 60 cm
• Plaster surfaces: tread (width*length) and riser (height*length)
• Rate = Rs 4 per 100 sq cm

Concept / Approach:
Area per stair = (tread area) + (riser area). Total area = (area per stair) * 50. Cost = (total area / 100) * 4.

Step-by-Step Solution:
Tread area per stair = 30*60 = 1800 sq cm Riser area per stair = 20*60 = 1200 sq cm Total plaster area per stair = 1800 + 1200 = 3000 sq cm Total plaster area for 50 stairs = 3000*50 = 150000 sq cm Number of 100 sq cm blocks = 150000/100 = 1500 Cost = 1500 * 4 = Rs 6000

Verification / Alternative check:
Rate per sq cm is Rs 4/100 = Rs 0.04. Multiplying 150000 * 0.04 also gives Rs 6000, confirming the same result by an alternate method.

Why Other Options Are Wrong:
Rs 4680 and Rs 5480 come from missing one face (tread or riser) or using wrong stair count. Rs 7600 and Rs 7000 result from adding extra faces or applying rate per sq cm incorrectly.

Common Pitfalls:
Mixing up width and length, forgetting to multiply by 50 stairs, or treating Rs 4 per 100 sq cm as Rs 4 per sq cm.

Final Answer:
The total expenditure is Rs 6000.