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The dimension of Mr. Narula’s bedroom is $8 m \times 7 m \times 5 m$ .It has two windows, each measuring $2 m \times 1 m$ and one door measuring $3 m \times 1 m$ .Find the cost of white washing the room at Rs. 50 per square meter.

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Rs. 12,750

Rs. 12,670

Rs. 14,250

Rs. 21,246

answer is A.

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Detailed Solution

Concept- Using formula for area of cuboid which is

A = 2 (lb + bh + lh)

,where

lb = length \times breadth

bh = breadth \times height

lh = length \times height

Given is that:
The room is of dimension

8 m \times 7 m \times 5 m

.Therefore,

Length = 8 m

Breadth = 7 m

Height = 5 m

And, dimensions of door (D) and windows (W):

D = 3 m \times 1 m

W = 2 m \times 1 m

Now finding area of the room,

Total area of bedroom = A = 2 (lb + bh + lh)

= 2 [(8 \times 7) + (7 \times 5) + (8 \times 5)]

= 2 [56 + 35 + 40]

= {2 \times 131 m}^{2}

A = {262 m}^{2}

According to the question, the bedroom needs to be white washed. Since white washing is not applied over doors and windows.
Therefore,

Area of door (D_{A}) = 3 m \times 1 m = {3 m}^{2}

Area of 2 windows (W_{A}) = 2 (2 m \times 1 m) = {4 m}^{2}

Now, area left for white washing would be:
Total area of bedroom-area of door+area of windows
=

A - (D_{A} + W_{A})

{262 m}^{2} - ({3 m}^{2} + {4 m}^{2})

{262 m}^{2} - {7 m}^{2}

{262 m}^{2} - {7 m}^{2}

{255 m}^{2}

Now for the total cost, given is that:
Cost of white washing

{1 m}^{2} of room = Rs . 50

∴ Cost of white washing {255 m}^{2} of room = 255 \times Rs . 50

= Rs . 12, 750

Hence, the correct option is 1.

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