A room is $7 m$ long and $5 m$ broad and it has a door measuring $2 m$ by $1.5 m$ and two windows each measuring $1.5 m$ by $1 m$ . The cost of painting the walls at $R s . 12.50$ per sq.m is $R s . 825$ . Find the height of the room.

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Solution

Area of the walls to be painted $=$ Area of $4$ faces of the room - Area of the door $-$ Area of $2$ windows
$= (7 \times h) + (7 \times h) + (5 \times h) + (5 \times h) - (2 \times 1.5) - (1.5 \times 1) - (1.5 \times 1) = 24 h - 3 - 3 = 24 h - 6$
Area of wall painted $= \frac{T o t a l c o s t o f p a i n t i n g t h e w a l l}{C o s t o f p a i n t i n g 1 s q . m o f t h e w a l l}$
$= \frac{825}{12.5} = 66 s q . m$
Thus, $24 h - 6 = 66$
$\Rightarrow$ $24 h = 72$
$\Rightarrow$ $h = \frac{72}{24} = 3 m$
Thus the height of the room is $3 m$ .

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A room is7 m long and 5 m broad and it has a door measuring 2 m by 1.5 m and two windows each measuring 1.5 m by 1 m. The cost of painting the walls at Rs. 12.50 per sq.m is Rs. 825. Find the height of the room.

A room is $7 m$ long and $5 m$ broad and it has a door measuring $2 m$ by $1.5 m$ and two windows each measuring $1.5 m$ by $1 m$ . The cost of painting the walls at $R s . 12.50$ per sq.m is $R s . 825$ . Find the height of the room.