Question 53

The sum of the dimensions of a room (i.e. length, breadth and height) is 24 metres and its length, breadth and height are in the ratio of 8: 7 : 5 respectively. If the room is to be painted at the rate of Rs. 12 per m2, what would be the total cost incurred on painting only the four walls of the room (in Rs.)?

Solution

Let the dimension of the room be $$8x , 7x , 5x$$ metres

Acc. to ques, => $$8x + 7x + 5x = 24$$

=> $$x = \frac{24}{20} = 1.2$$ metres

Curved surface area of the room = $$2 h (l + b)$$

= $$2 \times 5x \times (8x + 7x) = 10x \times 15x$$

= $$150 (x)^2 = 150 \times (1.2)^2$$

= $$150 \times 1.44 = 216 m^2$$

$$\therefore$$ Total cost incurred on painting only the four walls of the room = $$12 \times 216$$

= $$Rs. 2,592$$

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