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When the length of a rectangle A is reduced by 4 cm, while keeping the area constant, rectangle B is formed. The breadth of B is 12 cm. If the length of B is increased by 6 cm, again keeping the area constant, rectangle C is formed and its breadth is 4 cm less than that of B. What is the area of each rectangle?
  • a)
    96 cm2
  • b)
    144 cm2
  • c)
    168 cm2
  • d)
    180 cm2
  • e)
    270 cm2
Correct answer is option 'B'. Can you explain this answer?
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When the length of a rectangle A is reduced by 4 cm, while keeping the...
Let the length of A be / cm and breadth be b cm.
Area of A = / b ... (i) Length and breadth of B is (/ - 4) cm and 12 cm respectively.
Area of B = ( / - 4) x 12 ... (ii) Length of C is (/ - 4) + 6 = (/ + 2) cm and breadth of C is 12 - 4 = 8 cm Area of C = (/ + 2) x 8 ... (iii)
Since each rectangle has the same area, (/ - 4) x 12 = (/ + 2) x 8 3 / - 12 = 2 /+ 4
So  / = 1 6.
Area of each rectangle = (/ - 4) * 12 = 12 * 12 =144 cm2. Hence, option 2.
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When the length of a rectangle A is reduced by 4 cm, while keeping the...
Given Information:
- Length of rectangle A is reduced by 4 cm to form rectangle B.
- Breadth of rectangle B is 12 cm.
- Length of rectangle B is increased by 6 cm to form rectangle C.
- Breadth of rectangle C is 4 cm less than that of B.

Let's calculate the area of each rectangle:

- Let the length of rectangle A be x cm and breadth be y cm.
- Area of rectangle A = x * y

- Length of rectangle B = (x-4) cm
- Breadth of rectangle B = 12 cm
- Area of rectangle B = (x-4) * 12

- Length of rectangle C = (x-4+6) = (x+2) cm
- Breadth of rectangle C = 12-4 = 8 cm
- Area of rectangle C = (x+2) * 8

Equating the areas of rectangles A, B, and C:

- x * y = (x-4) * 12
- x * y = (x+2) * 8

Solving the above equations:
- xy = 12x - 48
- xy = 8x + 16

Subtracting the second equation from the first:
12x - 48 = 8x + 16
4x = 64
x = 16

Substitute x = 16 back into the equation xy = 12x - 48:
16y = 12*16 - 48
16y = 192 - 48
16y = 144
y = 9

Therefore, the area of each rectangle is:
- Area of rectangle A = 16 * 9 = 144 cm^2
- Area of rectangle B = 12 * 12 = 144 cm^2
- Area of rectangle C = 18 * 8 = 144 cm^2

Hence, the correct answer is option b) 144 cm^2.
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Each question is followed by two statements, A and B. Answer each question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q. If the breadth of a rectangle is increased by 2 units and the length is decreased by 3 units, the area is unchanged. What is the area of the rectangle?A. If the breadth is decreased by 1 unit and the length is increased by 3 units, the area remains the same.B. If the breadth is increased by 1 unit and the length is increased by 2 units, the area gets doubled.

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When the length of a rectangle A is reduced by 4 cm, while keeping the area constant, rectangle B is formed. The breadth of B is 12 cm. If the length of B is increased by 6 cm, again keeping the area constant, rectangle C is formed and its breadth is 4 cm less than that of B. What is the area of each rectangle?a)96 cm2b)144 cm2c)168 cm2d)180 cm2e)270 cm2Correct answer is option 'B'. Can you explain this answer?
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When the length of a rectangle A is reduced by 4 cm, while keeping the area constant, rectangle B is formed. The breadth of B is 12 cm. If the length of B is increased by 6 cm, again keeping the area constant, rectangle C is formed and its breadth is 4 cm less than that of B. What is the area of each rectangle?a)96 cm2b)144 cm2c)168 cm2d)180 cm2e)270 cm2Correct answer is option 'B'. 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 When the length of a rectangle A is reduced by 4 cm, while keeping the area constant, rectangle B is formed. The breadth of B is 12 cm. If the length of B is increased by 6 cm, again keeping the area constant, rectangle C is formed and its breadth is 4 cm less than that of B. What is the area of each rectangle?a)96 cm2b)144 cm2c)168 cm2d)180 cm2e)270 cm2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When the length of a rectangle A is reduced by 4 cm, while keeping the area constant, rectangle B is formed. The breadth of B is 12 cm. If the length of B is increased by 6 cm, again keeping the area constant, rectangle C is formed and its breadth is 4 cm less than that of B. What is the area of each rectangle?a)96 cm2b)144 cm2c)168 cm2d)180 cm2e)270 cm2Correct answer is option 'B'. Can you explain this answer?.
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