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DIRECTIONS for questions: Select the correct alternative from the given choices.
The breadth of a rectangle is decreased by 25%, as a result of which the perimeter of the rectangle decreased by 10%. By what percentage should the length of the rectangle now be increased, such that the perimeter of the rectangle will be the same as the initial one (i.e., before the breadth was decreased)?
  • a)
    12%
  • b)
    25%
  • c)
    20%
  • d)
    16.67%
Correct answer is option 'D'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the giv...
Given, Let the length and breadth be ℓ and b respectively.
2(ℓ + 0.75b) = 0.9 x (2(ℓ + b))
=> ℓ + 0.75b = 0.9ℓ + 0.9b
=>0.1 ℓ = 0.15b
=>ℓ : b = 3 :2
Let ℓ = 30 and b = 20
=> Present ℓ, b = (30, 15), i.e., after decrease in breadth.
Now, the length should be increased by 5 in order to compensate (i.e., retain ℓ + b = 30 + 20 = 50) for the decrease in breadth.
Hence 5 / 30 x 100 = 16.67%
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DIRECTIONS for questions: Select the correct alternative from the giv...
Calculation:
- Let the initial length of the rectangle be L and initial breadth be B.
- Initially, Perimeter = 2(L + B)

Given:
- After decreasing breadth by 25%, new breadth = 0.75B
- Perimeter decreased by 10%, new perimeter = 0.9(2(L + 0.75B))

Solving for L in terms of B:
- From initial perimeter: 2(L + B) = 0.9(2(L + 0.75B))
- Simplifying, we get L = 5B/4

Calculating the new length:
- To make the new perimeter equal to the initial one: 2(L + B) = 0.9(2(5B/4 + 0.75B))
- Solving, new length = 25B/16

Percentage increase in length:
- Percentage increase = ((new length - initial length) / initial length) * 100%
- Substituting values, we get percentage increase = ((25B/16 - 5B/4) / 5B/4) * 100%
- Percentage increase = (5B/16) / (5B/4) * 100% = 16.67%
Therefore, the length of the rectangle now should be increased by 16.67% to maintain the initial perimeter.
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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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DIRECTIONS for questions: Select the correct alternative from the given choices. The breadth of a rectangle is decreased by 25%, as a result of which the perimeter of the rectangle decreased by 10%. By what percentage should the length of the rectangle now be increased, such that the perimeter of the rectangle will be the same as the initial one (i.e., before the breadth was decreased)?a) 12%b) 25%c) 20%d) 16.67%Correct answer is option 'D'. Can you explain this answer?
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