Word Problems/Mathematics


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 bookshelf.
Sir please explain each point of this question and quickly I have exam tomorrow.

I'm sorry I didn't get to this in time, but I still must respond to all questions I receive.

Since the height is 110 cm, the breadth is 85 cm, and the depth is 25 cm, and the thickness of the wood is 5 cm, this makes the inside dimension 100 cm x 75 cm x 20 cm.  Note that for the height there is the top and bottom and for the width there is the left side and right side.  For the depth, however, there is only a back for most bookshelves I've seen don't have a front cover on them.

On the two sides at 110 x 25 = 2,750, so 2 x 2,750 = 5,500.
For the inside, we would have 100 X 20 = 2,000, so 2 x 2,000 = 4,000.

On the top and bottom we would have 2 x 25 x 85 = 4,250.
The inside would be 2 x 20 x 75 = 3,000.

On the back on the inside, we would have 100 x 75 = 7,500.
I won't worry about the back since its probably going to be against a wall.

On the front surface of the sides and top, the dimension could be thought of as the difference between two rectangles.  That gives 110 x 85 - 100 x 75 = 9,350 - 8,500 = 850.  I assume this is to be polished.

The sum of polished surfaces is 5,500 + 4,250 + 850 = 10,600. Since it cost 10 paise for each, the total cost would be 106,000 paise.

The sum of the painted surface is 4,000 + 3,000 + 7,500 = 14,500.
As 20 paise per cm2, that would gives 290,000 paise.

The total is then 106,000 paise + 290,000 paise = 396,000 paise.

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Scott A Wilson


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