Aptitude - Area - Discussion

40*3=120
60*3=180
TOTAL=300
LESS=291
BALANCE=9 SQCM
THAT IS 3*3
ANS=3.

Cosidering Road parallel to 60m side Area :- 60x.
Cosidering Road parallel to 40m side Area :- 40x.

Common area :- x*x.

Hence :- 291=60x+40x-x*x.

The road is in the shape of plus mark.

So area of 1st road is 60x.

So area of 2nd road is 40x.

But in the middle the square has been calculated twice above. So subtract that area x^2.

There is no intercrossing left. When we considered 60x +40x, aren't we considering the intercrossing too? Otherwise the lengths couldn't have been 60 and 40.

Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291.

x2 - 100x + 291 = 0.

(x - 97)(x - 3) = 0.

x = 3.

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.

@Rkbm your answer best answer.

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

@Puskar,

You may go through Diego's answer for better understanding.

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.