LIC AAO 22 Mar 2015 Paper

Question : 49 of 160

Marks: +1, -0

A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn, which has an area of 240 sq. m. If the width of the path is 3m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot? (in sq. m.)

Validate

Solution:

Let the width of plot be x metre
∴ Length = (x + 2) metre
Area of cocrete path = 3x sq metre
According to the question,
x (x + 2) - 3x = 240
⇒

x^2

- x - 240 = 0
⇒

x^2

- 16x + 15x - 240 = 0
⇒ x (x - 16) + 15 (x - 16) = 0
⇒ (x - 16) (x + 15) = 0
⇒ x = 16 because x ≠ - 15
∴ legth = 16 + 2
= 18 metre
∴ Area of plot = 18 × 16

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