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A wooden bookshelf has external dimensions as follows, height = 110 cm, depth = 25 cm, 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 book shelf.

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Rs. 6560

Rs. 3212

Rs. 6300

Rs. 6275

answer is D.

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Detailed Solution

Given, the height of the bookshelf = 110cm.
depth = 25 cm, breadth = 85 cm
Thickness of plank

= 5

cm.
Below is the figure of the bookshelf,
Question Image

Let the height of the open portion = h.
So, the height of the open portion be,

110 = 3 h + 4 × 5

110 − 20 = 3 h

90 = 3 h

h = 30

cm
Length of bookshelf

= 85

cm.
Thickness of plank

= 5

cm.
Therefore,

85 = l + 2 × 5

85 − 10 = l

l = 75

cm
The dimensions of bookshelf are,
Length l = 85cm,
Breadth b = 25cm and
Height h = 110cm.
Area to be polished = Total surface area of bookshelf (cuboid)

− 3 ×

Area of open portion (rectangle)
We know that total surface area of cuboid is

2 l b + b h + l h

and area of rectangle is

l × b

⇒ 2 (85 × 25 + 25 × 110 + 110 × 85) − 3 × (75 × 30)

⇒ 2 (2125 + 2750 + 9350) − 3 (2250)

⇒ 28450 − 6750

⇒ 21700 c m 2

Cost of polishing will be,

⇒ 20 × 21700

paise

⇒ 434000

paise

⇒ R s 434000100

⇒ R s

4340
Total area to be painted

= 3 ×

(Total area of internal of shelf -Area of open portion) ,
length = 75, height = 30 and breadth =(25-5)=20

⇒ 3 × [2 (30 × 75 + 75 × 20 + 20 × 30) − (30 × 75)]

⇒ 3 × [2 (4350) − 2250]

⇒ 3 × (8700 − 2250)

⇒ 3 × 6450

⇒ 19350 c m 2

Cost of painting =

19350 c m 2 = 19350 × 10

paise

⇒ 193500

paise

⇒ R s 193500100

⇒ R s

1935
Total expenses = Cost of polishing + Cost of painting

⇒ 4340 + 1935

⇒ R s

6275
Therefore, the correct option is 4.

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