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A rectangular room has to be painted along with the ceiling. The cost of painting another rectangular room whose breadth, length and height are respectively 20% more, 5% less and 10% less than the first room is Rs. 4,512. If the ratio of length, breadth and height of the first room is 4 : 1 : 2, what is the cost of painting the first room? Assume that the rate of painting the two rooms (in Rs. per square feet) is the same.
  • a)
    Rs. 4,300
  • b)
    Rs. 4,400
  • c)
    Rs. 4,900
  • d)
    Rs. 4,800
  • e)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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A rectangular room has to be painted along with the ceiling. The cost ...
Let the length, breadth and height of the first room be l, b and h feet respectively.
So, length, breadth and height o f the second room are 0.95l, l.2 b and 0.9h respectively.
For the first room, l:b:h = 4 : 1 : 2
Let l, b and h be 4x, x and 2x respectively.
So, length, breadth and height of second room become 3.8x, 1.2x and 1.8x respectively.
Area of the walls and ceiling of the first room that is to be painted = 2h(l + b) + lb
= 2 x 2x (4x + x) + (4x x x)
= 24x2
Area of the walls and ceiling of the second room that is to be painted = 2h(l + b) + lb
= 2 x 1.8x (3.8x + 1.2x) + (3.8x x 1.2x) = 22.56x2
Now cost of painting the second room is Rs. 4,512. 22.56.x1 2 3 = 4512
Thus, cost o f painting the first room is R s. 4 ,800 .
Hence, option 4.
 
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A rectangular room has to be painted along with the ceiling. The cost ...
Given:
Ratio of length, breadth, and height of the first room = 4:1:2

Let the length, breadth, and height of the first room be 4x, x, and 2x respectively.

The cost of painting the first room = Area of the room * Rate per square feet

Area of the first room = 2(lb + bh + lh) = 2[(4x)(x) + (x)(2x) + (4x)(2x)] = 2[4x^2 + 2x^2 + 8x^2] = 2(14x^2) = 28x^2

Now, the dimensions of the second room are 20% more, 5% less, and 10% less than the first room.

The length of the second room = 4x + (20/100)(4x) = 4x + (4/5)x = (24/5)x

The breadth of the second room = x - (5/100)(x) = x - (1/20)x = (19/20)x

The height of the second room = 2x - (10/100)(2x) = 2x - (1/10)(2x) = (19/20)2x = (38/20)x = (19/10)x

The cost of painting the second room = Area of the second room * Rate per square feet

Area of the second room = 2[(24/5)x][(19/20)x + x + (38/20)x] = 2[(24/5)(19/20)x^2] = 2(19/5)x^2

Given that the cost of painting the second room is Rs. 4,512, we can write:

2(19/5)x^2 * Rate per square feet = 4,512

Rate per square feet = 4,512 * 5/(2 * 19 * x^2)

Now, substituting the value of x in terms of the breadth of the first room:

Rate per square feet = 4,512 * 5/(2 * 19 * (1/4)x^2) = 2,256 * 5/(19 * (1/16)x^2)

Rate per square feet = 2,256 * 5/(19 * (1/16)(x^2/1)) = 2,256 * 5 * 16/(19 * x^2)

Rate per square feet = 240

Now, using the rate per square feet, we can calculate the cost of painting the first room:

Cost of painting the first room = Area of the first room * Rate per square feet = 28x^2 * 240 = 6,720x^2

Substituting the value of x = (breadth of the first room) = (1/4)x = (1/4)(x/1) = x/4

Cost of painting the first room = 6,720(x/4)^2 = 6,720(x^2/16) = 420x^2

Since x represents the breadth of the first room, we can conclude that the cost of painting the first room is directly proportional to the square of its breadth.

Therefore, the cost
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A rectangular room has to be painted along with the ceiling. The cost of painting another rectangular room whose breadth, length and height are respectively 20% more, 5% less and 10% less than the first room is Rs. 4,512. If the ratio of length, breadth and height of the first room is 4 : 1 : 2, what is the cost of painting the first room? Assume that the rate of painting the two rooms (in Rs. per square feet) is the same.a)Rs. 4,300b)Rs. 4,400c)Rs. 4,900d)Rs. 4,800e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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A rectangular room has to be painted along with the ceiling. The cost of painting another rectangular room whose breadth, length and height are respectively 20% more, 5% less and 10% less than the first room is Rs. 4,512. If the ratio of length, breadth and height of the first room is 4 : 1 : 2, what is the cost of painting the first room? Assume that the rate of painting the two rooms (in Rs. per square feet) is the same.a)Rs. 4,300b)Rs. 4,400c)Rs. 4,900d)Rs. 4,800e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A rectangular room has to be painted along with the ceiling. The cost of painting another rectangular room whose breadth, length and height are respectively 20% more, 5% less and 10% less than the first room is Rs. 4,512. If the ratio of length, breadth and height of the first room is 4 : 1 : 2, what is the cost of painting the first room? Assume that the rate of painting the two rooms (in Rs. per square feet) is the same.a)Rs. 4,300b)Rs. 4,400c)Rs. 4,900d)Rs. 4,800e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular room has to be painted along with the ceiling. The cost of painting another rectangular room whose breadth, length and height are respectively 20% more, 5% less and 10% less than the first room is Rs. 4,512. If the ratio of length, breadth and height of the first room is 4 : 1 : 2, what is the cost of painting the first room? Assume that the rate of painting the two rooms (in Rs. per square feet) is the same.a)Rs. 4,300b)Rs. 4,400c)Rs. 4,900d)Rs. 4,800e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
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