Question:medium

If the length of a rectangle is increased by 5 cm and the breadth is decreased by 5 cm, area of the rectangle remained same. What are the dimensions of the given rectangle?
Statement 1: If the length is decreased by 12 cm and the breadth increased by 8 cm, even then the area is unaltered
Statement 2: Breadth of the rectangle is 4 less than twice its length
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer

Updated On: Jul 21, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is D

Solution and Explanation

The correct answer is option (D):
either statement (1) alone or statement (2) alone is sufficient to answer the question

Let's analyze the problem and the statements to determine if we can find the dimensions of the rectangle.

Problem: The length is increased by 5 cm and the breadth is decreased by 5 cm, and the area remains the same. Let's denote the original length as 'l' and the original breadth as 'b'. The original area is l*b. The new area is (l+5)(b-5). Since the area remains the same:
(l+5)(b-5) = l*b
lb - 5l + 5b - 25 = lb
-5l + 5b - 25 = 0
-5l + 5b = 25
Dividing by 5, we get:
-l + b = 5
b = l + 5 (Equation 1)

Now, let's look at the statements:

Statement 1: If the length is decreased by 12 cm and the breadth increased by 8 cm, the area is unaltered.
This means (l-12)(b+8) = l*b
lb + 8l - 12b - 96 = lb
8l - 12b - 96 = 0
8l - 12b = 96
Dividing by 4, we get:
2l - 3b = 24 (Equation 2)

We now have two equations with two variables (Equation 1 and Equation 2). We can solve these equations to find 'l' and 'b'. Therefore, Statement 1 alone is sufficient.

Statement 2: Breadth of the rectangle is 4 less than twice its length.
This translates to:
b = 2l - 4 (Equation 3)

We already have Equation 1: b = l + 5.
We now have two equations with two variables (Equation 1 and Equation 3). We can solve these equations to find 'l' and 'b'. Therefore, Statement 2 alone is sufficient.

Since either statement 1 or statement 2 alone is sufficient to solve the problem, the correct answer is:
either statement (1) alone or statement (2) alone is sufficient to answer the question

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Top Questions on Statements and Inferences

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  • IBSAT
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  • IBSAT
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