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Aptitude - Area - Discussion

Discussion Forum : Area - General Questions (Q.No. 5)
Area
5.
A rectangular park 60 m long and 40 m 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 sq. m, then what is the width of the road?
2.91 m
3 m
5.82 m
None of these
Answer: Option
Explanation:

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.

Video Explanation: https://youtu.be/R3CtrAKGxkc

Discussion:
75 comments Page 5 of 8.
Nakul gowda said:   2 decades ago
60x + 40x includes the intersection part twice..so to include the intersection part only once, subtract area of intersection part once, ie, x^2....got it yet..
Sujay ramesh said:   2 decades ago
Thanks ayoosh. Your explanation is good :).
Jhola said:   2 decades ago
Very good ayoosh.
Naju said:   2 decades ago
Draw the figure you can c two cross road intersect, so we need to subtract it.
Tanya said:   2 decades ago
Its because the area of 2 roads has come out to be 291m2. Rest of the explaination has been given by prajwal.
Shreya said:   2 decades ago
My doubt is

60x+40x-x2=291?.
Prajwal said:   2 decades ago
I got it. Its because. 60 and 40 get multiplies to width and. Since there are two cross roads. There will be a common space for two roads. (width of two cross roads is width^2).
Rajan said:   1 decade ago
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.
Sri said:   1 decade ago
@Ayoosh good explanation.
Raji said:   1 decade ago
@Aysooh superb yar
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