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A hall $36 m$ long and $24 m$ broad allowing $80 m 2$ for doors and windows, the cost of preparing the wall at ₹ 8.40 per $m 2$ is ₹ $9408$ . Find the height of the hall.

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20 m

10 m

30 m

15 m

answer is B.

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Detailed Solution

The hall will be made of 4 walls. The length of the opposite wall will be the same. And the height of all the 4 walls will be the same.

l = 36 m

b = 24 m

Area of doors and windows is given to be

A d = 80 m 2 ....... (1)

)
Now, the area of the two adjacent walls will be equal to

l h + b h

..
∴ Area of all the walls of the hall will be

A = 2 (l h + b h)

⇒ A = 2 (l + b) h ⇒ A = 2 (36 + 24) h ⇒ A = 120 h m 2 ......... (2)

From equations (1) and (2)
Area of wall excluding the area of the windows and doors is given as

A − A d = (120 h − 80) m 2 ......... (3)

Cost of preparing the walls at ₹ 8.40 per

m 2

= ₹

9408

. . . . . . (4)
From equation (3) and (4), we can say that the cost of preparing the complete area of the walls is given by,

⇒ 120 h − 80 × 8.40 = 9408 ⇒ 1008 h − 672 = 9408

Rearranging it we can write

1008 h = 9408 + 672 ⇒ 1008 h = 10, 080 ∴ h = 10, 080 1008 ⇒ h = 10 m

Hence, the height of each wall will be 10 m.

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