question_answer

A rectangular plot 55 m long and 45 m broad, has two concrete crossroads (of equal width) running in the middle of it. One parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the area of the lawn is \[1911\,{{m}^{2}},\] what is the width of each of the crossroads?                                                      [SBI (PO) 2015]

A) 5 m                              

B) 5.5 m

C) 6 m      

D) 4 m

E) 4.5 m

Correct Answer: C

Solution :

Given, length = 55 m and breadth = 45 m

Area of lawn \[=1911\,{{m}^{2}}\]

Area of rectangular plot \[=45\times 55=2475\,{{m}^{2}}\]

Area of crossroads \[=2475-1911=564\,{{m}^{2}}\]

Let the width of the crossroads = x m

\[\therefore \]      \[45x+55x-{{x}^{2}}=564\]

\[\Rightarrow \]   \[{{x}^{2}}-100x+564=0\]

\[\Rightarrow \]   \[{{x}^{2}}-94x-6x+564=0\]

\[\Rightarrow \]   \[x\,(x-94)-6\,(x-94)=0\]

\[\Rightarrow \]   \[(x-6)(x-94)=0\]

\[\Rightarrow \]               \[x=6,\]94

[here, 94 is discarded]

\[\therefore \]                  \[x=6m\]