A rectangular football field is fenced on all four sides. The length

Question

A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 25% of its original value and fence the field again.. What will be the cost of the new fencing?

A) $360
B) $180
C) $425
D) $405
E) $415

A) $360
B) $180
C) $425
D) $405
E) $415

Lampard42 · Answer

L=2B; cost of fencing 2(L+B)*Cost per unit = 360$; Sub L=2B in this gives 2(3B)*Cost per unit = 360$; B*Cost per unit = 60$ and L*Cost per unit = 120$; if B is increased by 50% B*Cost per unit = 60*1.5 = 90 and L*Cost per unit = 120*3/4 = 90; So Cost of the new field is 2*(90+90) = 360$ IMO Option A

urshi · Answer

Current design :
L - 2x
B - x

Perimeter = 2(2x + x) = 6x
Cost for 6x = $360

New design :
L - 75/100 * 2x = 1.5x
B - 150/100 * x = 1.5x

Perimeter = 2(1.5x + 1.5x) = 6x
Since the perimeter remains unchanged, cost of fencing also remains unchanged,$360 .OPTION A is the answer.

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Archit3110 · Answer

intital cost ;
w=1
l=2
2*3*x=360
x=60
new dimension
l=1.5 and w=1.5
2*3*60=360
IMO A

CrackverbalGMAT · Answer

A good question that tests you, not only on the basic property of a rectangle but also on percentage change concepts!

If the breadth of the field is 2x yards, then the length of the field is 4x yards. The perimeter of the field, which in essence is the length of the fence, will be 12x yards. So, we can say that it costs us $360 to fence 12x yards.

Now, the new breadth will be 3x (150% of 2x) and the new length will also be 3x (75% of 4x). We now have a square field. The perimeter of this field is naturally 4 times each side, which turns out to be 12x. The cost of the fencing will still remain $360.

The correct answer option is A.

While assuming values, notice how we have assumed the breadth to be 2x and length to be 4x. This is to ensure that, when we apply the percentages on them, they don’t result in fractions and calculations become simpler.

Hope this helps!

ScottTargetTestPrep · Answer

We can let the breadth of the original field be 60 ft, and thus the length is 120 ft and the perimeter of is (60 + 120) x 2 = 360 ft. Thus, it would cost 360/360 = $1 per foot to fence the field.

Now, the breadth of the new field is 60 x 1.5 = 90 ft and the length is 120 x 0.75 = 90 ft and the perimeter is (90 + 90) x 2 = 360 ft. We see that the perimeter doesn’t change, so it would still cost $360 to fence it.

Answer: A

A rectangular football field is fenced on all four sides. The length

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A rectangular football field is fenced on all four sides. The length

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