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Question:

A wooden bookshelf has external dimensions as follows: Height=110 cm, Depth=25 cm, and Breadth=85 cm. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm², find the total expenses required for polishing and painting the surface of the bookshelf.

Solution:

Let the external dimensions of the bookshelf be:
Height (H) = 110 cm
Depth (D) = 25 cm
Breadth (B) = 85 cm
Thickness of the plank (t) = 5 cm

External surface area to be polished:
2(H x B) + 2(H x D) + 2(B x D) = 2(110 x 85) + 2(110 x 25) + 2(85 x 25) = 18700 + 5500 + 4250 = 28450 cm²
Cost of polishing = 28450 cm² x 20 paise/cm² = 569000 paise = Rs. 5690

Internal dimensions:
Height (h) = 110 - 2(5) = 100 cm
Depth (d) = 25 - 2(5) = 15 cm
Breadth (b) = 85 - 2(5) = 75 cm

Internal surface area to be painted:
2(h x b) + 2(h x d) + 2(b x d) = 2(100 x 75) + 2(100 x 15) + 2(75 x 15) = 15000 + 3000 + 2250 = 20250 cm²
Cost of painting = 20250 cm² x 10 paise/cm² = 202500 paise = Rs. 2025

Total expenses = Cost of polishing + Cost of painting = Rs. 5690 + Rs. 2025 = Rs. 7715

Therefore, the total expenses required for polishing and painting the surface of the bookshelf is Rs. 7715.