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RAS question

A rectangular garden of dimensions 60 m × 40 m has a path of width 2 m all around it. The area of the path is:

Correct answer: (C) 416 m².

The area of the 2 m wide path around a 60 m by 40 m rectangular garden is 416 m².

  1. (A)

    480 m²

  2. (B)

    400 m²

  3. (C)

    416 m²

  4. (D)

    408 m²

Explanation

For a rectangular path running all around a rectangular garden, first calculate the outer rectangle and then subtract the garden itself. The garden is 60 m by 40 m, so its area is 60 × 40 = 2,400 m². A 2 m path on every side adds 4 m to each dimension: 2 m on the left and 2 m on the right, and likewise at the top and bottom. The outer dimensions are therefore 64 m by 44 m, giving an outer area of 64 × 44 = 2,816 m². NCERT uses the same principle for rectangular paths: area of the path equals outer rectangle area minus inner rectangle area. Hence the path area is 2,816 − 2,400 = 416 m².

Why the other options are wrong

  • (A) 480 m² would overstate the path area; it does not match the difference between the 64 m × 44 m outer rectangle and the 60 m × 40 m garden.
  • (B) 400 m² ignores the extra corner area created when the path expands both dimensions by 2 m on each side.
  • (D) 408 m² is close but arithmetically off, because 2,816 − 2,400 is 416, not 408.

Concept

This tests mensuration, especially the area of a rectangle and the subtraction method for paths around rectangular fields. It recurs in RAS because such questions check quick, reliable handling of dimensions, units and boundary cases.

Source

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