Aptitude - Area - Discussion

@All.

Take:
(60-x) * (40-x).
We gets the remaining area,
Already in the questions, it gives that remaining area is 2109 m2,

Verify the equation with 3.
The equation will be satisfied.

We can also subtract the width of the road from length and breadth of the road and multiply the values to get the area of the lawn i.e.

Let the width be x.

Length of lawn = 60 - x.

Breadth of lawn = 48 - x.

(60 - x) (40 - x) = 2109. As given in question.

X^2 - 100x - 291 = 0.

X = 3 and 97.

The value 3 is there in the given option. So, width of the road is 3m.

So it is a rectangle of 60x40cm. It has 2 crossroads, therefore the area of the roads is the horizontal one: 60 times the with (x). -->60*x plus the vertical road 40*x. This results in 60x+40x but you are adding 2 times the area where the roads intersect (one time for the vertical road and one time for the horizontal road). The double counted area is x*x = x^2. So if you subtract this area from 60x+40x you will eliminare 60x+40x -x^2.

                       60cm
_______________________________
I     LAWN        I RD I       LAWN          I
I______________I____I________________I
I    ROAD         I       I      ROAD          I
I_____________  IX^2I________________I  40cm
I     LAWN        I       I       LAWN         I
I______________I RD I________________I

Hope this helps you better understand the problem.

@All.

Please draw the picture first.

Two roads intersecting each other like " + " sign not like "x" sign. One road has an area of 60x other one has 40x. There is a common area of x^2.

Use formula,
X+Y+(X*Y/100) for an increase in length and breadth of any quadrilateral.

Which is,

=20+20+(20*20/100)
=20+20+4
=44%.

Why only square of width is taken and not length?

Thanks all for explaining the answer in detail.

Good job @Ayoosh.

Guys! it should be 2x^2 instead of simply x^2? don't you all agree?

Great explanation @Ayoosh.