SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 56 of 100

Marks: +1, -0

A rectangular park 60 metre long and 40 metre wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 metre2 then the width of the road is

3 metre
5 metre
6 metre
2 metre

Validate

Solution:

(1)

Area of rectangular park = 60 × 40 = 2400 sq. metre
Let the width of cross-road be x metre.
∴ Area of cross-roads

=60 x+40 x-x^{2}

=100 x-x^{2}

According to the question,

100 x-x^{2}=2400-2109

⇒100 x-x^{2}=291

⇒x^{2}-100 x+291=0

⇒x^{2}-3 x-97 x+291=0

⇒x(x-3)-97(x-3)=0

⇒(x-3)(x-97)=0

⇒x=3

because

x ≠ 97

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