Quantitative Aptitude Ques 2464

Question: 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,m^{2}. $ If the width of the path is 3 m and the length of the plot is greater than its breadth by 2 m, what is the area of the rectangular plot? [LIC (AAO) 2014]

Options:

A) $ 255,m^{2} $

B) $ 168,m^{2} $

C) $ 288,m^{2} $

D) $ 360,m^{2} $

E) $ 224,m^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Given, width of path = 3 m Area of plot (excluding path) $ =240,m^{2} $ Let breadth of plot = x Length of plot $ =x+2 $ According to the question, $ 240=x,(x+2)-3\times x $

$ \Rightarrow $ $ 240=x^{2}-x $

$ \Rightarrow $ $ x^{2}-x-24=0 $

$ \Rightarrow $ $ x^{2}-16x+15x-24=0 $

$ \Rightarrow $ $ x,(x-16)+15,(x-16)=0 $

$ \Rightarrow $ $ (x-16)(x+15)=0 $

$ \therefore $ $ x=16 $

$ \therefore $ Area of plot = Length $ \times $ Breadth $ =18\times 16=288,m^{2} $

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