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.