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The rectangular floor of a warehouse is 300 feet wide and 350 feet

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The rectangular floor of a warehouse is 300 feet wide and 350 feet [#permalink]

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The rectangular floor of a warehouse is 300 feet wide and 350 feet long. If the width remains fixed, how many additional feet would have to be added to the length to increase the floor area by 20 percent?

(A) 42
(B) 50
(C) 65
(D) 70
(E) 84
[Reveal] Spoiler: OA

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Re: The rectangular floor of a warehouse is 300 feet wide and 350 feet [#permalink]

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New post 26 Sep 2017, 00:57
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If the rectangular floor is 300*350 feet, the area of the floor is 105000 square feet.

If the width remains fixed,
how many feet must be added to length s.t the floor area increases by 20%(\(\frac{1}{5}\))

The increased area is \(\frac{6}{5}*105000 = 6*21000 = 126000\) (because \(1+\frac{1}{5}= \frac{6}{5}\))

Let the increased length be x.
Since the width remains the same, 300*x= 126000

x = 1260/3 = 420 which is an increase of 420-350=70(Option D)

P.S there are easier ways to do these questions. These lengthy calculation needn't be done.
More often than not in such questions, the common terms will cancel each other out :)
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Re: The rectangular floor of a warehouse is 300 feet wide and 350 feet [#permalink]

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New post 26 Sep 2017, 04:26
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The rectangular floor of a warehouse is 300 feet wide and 350 feet long. => Area = 300* 350

If the width remains fixed, how many additional feet would have to be added to the length to increase the floor area by 20 percent?
Let new measurement = 300 feet by (350+x)

New floor area = 1.2 * Old floor area <= 20% increase = (1+20/100) = 1.2 *Old area)

=>300 * (350+x) =1.2*(300*350)
=> 350 +x = 1.2*350
=> x= 350 * 1.2 - 350 = 350(1.2-1) = 350 * 0.2 = 70

Answer: D

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Re: The rectangular floor of a warehouse is 300 feet wide and 350 feet [#permalink]

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New post 26 Sep 2017, 23:18
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length of rectangular field = 350 feet
width of rectangular field = 300 feet
Area of rectangular field = length*width =350*300 sq.feet

let additional length of field be x.
hence,
new length= 350+x; new width=300
New area of field would be 20% more than that of original field.
Therefore,
(350+x)*(300) = 1.2*(300)*(350)
350+x=420
x=70

Hence Answer is Option D.

Kudos if it helps.

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Re: The rectangular floor of a warehouse is 300 feet wide and 350 feet [#permalink]

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New post 29 Sep 2017, 10:18
Bunuel wrote:
The rectangular floor of a warehouse is 300 feet wide and 350 feet long. If the width remains fixed, how many additional feet would have to be added to the length to increase the floor area by 20 percent?

(A) 42
(B) 50
(C) 65
(D) 70
(E) 84


The initial area is 300 x 350 = 105,000, so an increase of 20% would be 1.2 x 105,000 = 126,000. If we let n = the new length, we have:

300n = 126,000

n = 420

Thus, the length would have to be increased by 70 feet.

Alternate solution:

Since the width remains fixed, in order to increase the area by 20%, the length must be increased by 20% also. Thus, the new length should be 350 x 1.2 = 420 feet, an increase of 70 feet more than the original length.

Answer: D
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Re: The rectangular floor of a warehouse is 300 feet wide and 350 feet   [#permalink] 29 Sep 2017, 10:18
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