$A$ wooden bookshelf has external dimensions as follows: Height $= 110\, cm$,Depth $= 25\, cm$,Breadth $= 85\, cm$ (see Fig.). 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 $cm^2$ and the rate of painting is $10$ paise per $cm^2$,find the total expenses required for polishing and painting the surface of the bookshelf.

(A) $1$. External Surface Area to be polished:
External dimensions: $H = 110\, cm, B = 85\, cm, D = 25\, cm$.
External surface area (excluding the front face) $= 2(H \times D) + (B \times D) + 2(H \times B) = 2(110 \times 25) + (85 \times 25) + 2(110 \times 85) = 5500 + 2125 + 18700 = 26325\, cm^2$.
Area of the front face (excluding the openings) $= (110 \times 85) - 3(100 \times 75) = 9350 - 22500$ (This is not correct,let's re-evaluate).
Correct approach: External surface area to be polished $= 2(110 \times 25) + (85 \times 25) + 2(110 \times 85) - 3(100 \times 75) = 5500 + 2125 + 18700 - 22500 = 3825\, cm^2$.
$2$. Internal Surface Area to be painted:
Internal dimensions of each shelf: $H' = 30\, cm, B' = 75\, cm, D' = 20\, cm$.
Area of $3$ shelves $= 3 \times [2(H' \times D') + (B' \times D') + 2(H' \times B')] = 3 \times [2(30 \times 20) + (75 \times 20) + 2(30 \times 75)] = 3 \times [1200 + 1500 + 4500] = 3 \times 7200 = 21600\, cm^2$.
$3$. Total Expenses:
Cost of polishing $= 3825 \times 0.20 = ₹ 765$.
Cost of painting $= 21600 \times 0.10 = ₹ 2160$.
Total cost $= 765 + 2160 = ₹ 2925$.