Question

A rectangular room has to be painted on its four walls and the ceiling. The cost of painting another rectangular room with breadth which is 10% less, length which is 10% more and height which is 10% less than the dimensions of the first room is ₹1,872. How much will it cost to paint the first room given that for this room, the length, breadth and height are in the ratio 2 : 1 : 3?

(A) ₹1,956 (B) ₹2,000
(C) ₹2,100 (D) Cannot be determined

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Answer 1

Answer:

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Step-by-step explanation:

Answer 2

The cost to paint the first room is Rs 2100

Given,

The cost to paint the second room = is Rs 1872

The dimensions of the second room with breadth which is 10% less, length which is 10% more, and height which is 10% less than the dimensions of the first room.

The length, breadth, and height are in the ratio 2: 1 : 3

To find,

The cost to paint the first room

Solution,

Let the length, breadth, and height of the first room be l, b, and h respectively.

So, the length, breadth, and height of the second room are 1.1l, 0.9 b, and 0.9h respectively.

For the first room, l:b:h = 2 : 1 : 3

Let l, b, and h be 2x, x, and 3x respectively.

So, the length, breadth, and height of the second room become 2.2x, 0.9x, and 2.7x respectively.

The Area of the walls and ceiling of the first room that is to be painted = 2h(l + b) + lb

= 2 x 3x (2x + x) + (2x x x)

= 21x2

Area of the walls and ceiling of the second room that is to be painted = 2h(l + b) + lb

= 2 x 2.7x (2.2x + 0.9x) + (2.2x x 0.9x) = 18.72x2

Now the cost of painting the second room is Rs. 1872

Cost of painting the first room = (21 * 1872) / 18.72

= Rs 2100

Thus, the cost of painting the first room is Rs. 2100.

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