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Q.

The external dimensions of a wooden bookshelf are, height = 110 cm, depth = 25 cm and breadth = 85 cm. The plank is 5 cm thick everywhere. The external faces are to be polished and the inner faces are to be painted, the rate of polishing is 20paise per $cm 2$ and the rate of painting is 10paise per $cm 2$ . Then what will be the total expenses required for polishing and painting the surface of the bookshelf?

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a

Rs.6075

b

Rs.6200

c

Rs.6275

d

Rs.6270

answer is C.

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Detailed Solution

Question Image

Given that the external dimensions of a wooden bookshelf are, height = 110 cm, depth = 25 cm and breadth = 85 cm. The plank is 5 cm thick everywhere. The external faces are to be polished and the inner faces are to be painted, the rate of polishing is 20paise per

and the rate of painting is 10paise per

cm 2

.
The total surface area of a cuboid

= 2 l b + b h + h l

= 100 × 85 + 2 (110 × 25) + 2 (85 × 25) + 2 (110 × 5) + 4 (75 × 5)

= 9350 + 5500 + 4250 + 1100 + 1500

= 21700 c m 2

The total cost will be,

= 21700 × 20 100 = R s 4340

The internal surface,
= Total surface area - Area of the three cuboids

= 3 2 75 × 30 + 30 × 20 + 75 × 20 − 3 75 × 30 = 6 2250 + 600 + 1500 − 6750 = 19350 m 2

The cost of painting at the rate of Rs.10 per cm square will be,

= 19350 × 10 100 = R s 1935

The total cost will be,

= R s 4340 + R s 1935 = R s 6275

Thus, the total expense required is Rs.6275.
Therefore, the correct option is 3.

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The external dimensions of a wooden bookshelf are, height = 110 cm, depth = 25 cm and breadth = 85 cm. The plank is 5 cm thick everywhere. The external faces are to be polished and the inner faces are to be painted, the rate of polishing is 20paise per cm 2 and the rate of painting is 10paise per cm 2 . Then what will be the total expenses required for polishing and painting the surface of the bookshelf?