Question:medium

A path runs around a rectangular lawn. What is the width of the path?
Statement 1: The length and breadth of the lawn are in the ratio 3 : 1 respectively
Statement 2: The cost of constructing the path at Rs. 50 per sq.m is Rs. 8832

Updated On: Jan 13, 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
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The Correct Option is

Solution and Explanation

The correct answer is option (E):
Neither statement (1) nor statement (2) suffices to answer the question

Let's analyze why the correct answer is "Neither statement (1) nor statement (2) suffices to answer the question."

The core question asks for the width of the path around the rectangular lawn.

Statement 1: The length and breadth of the lawn are in the ratio 3:1.
This statement only gives us a ratio. Let the length be 3x and the breadth be x. We don't know the actual dimensions, nor do we have any information about the path's area or cost. Thus, statement 1 alone is insufficient.

Statement 2: The cost of constructing the path at Rs. 50 per sq.m is Rs. 8832.
This statement provides the total cost and the cost per square meter. We can calculate the total area of the path: 8832 / 50 = 176.64 sq.m. However, we don't know the dimensions of the lawn. We can't determine the width of the path just from the path's area. Therefore, statement 2 alone is insufficient.

Now, let's consider if we combine the statements. We still have the ratio of the lawn's length and breadth (3:1) and the area of the path (176.64 sq.m). Let's denote the width of the path as 'w'. The dimensions of the lawn are 3x and x. The dimensions of the outer rectangle (lawn + path) would be (3x + 2w) and (x + 2w). The area of the path can be calculated as the area of the outer rectangle minus the area of the lawn: (3x + 2w)(x + 2w) - 3x * x = 176.64
Expanding this gives us: 3x^2 + 6xw + 2xw + 4w^2 - 3x^2 = 176.64 which simplifies to 8xw + 4w^2 = 176.64.
We now have one equation (8xw + 4w^2 = 176.64) with two unknowns (x and w). We cannot solve this equation uniquely for 'w' given only this information.

Therefore, neither statement 1 nor statement 2 alone, nor both statements combined, provide enough information to determine the width of the path.
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