A rectangular park which is 20 feet long and 24 feet wide is to be fil : Problem Solving (PS)

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Bunuel

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A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 01:46

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Competition Mode Question

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 01:58

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Kudos

Expert Reply

Quote:

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

L = 20, B = 24, H (to be increased) = 2

Volume of Sand Needed = L*B*H = 20*24*2 = 960 Cubic feet

Question: 1200 is what percentage greater than 960

i.e. Required output = (1200-960)*100/960 = 25%

ANswer: Option C

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 02:20

1

Kudos

Given: Volume of sand available - \(1200 f^3\) .. \(L=20, B=24, H=2\)

Volume required to fill 2 feet - \(20*24*2 = 960 f^3\) \((L*B*H)\)

Extra: Sand available - Sand required .. \(1200-960 = 240\)

So, the percentage of extra: \(\frac{Extra*100 }{ Required}\) ... \(\frac{240 * 100 }{ 960}= 25\)%

'C' is the Winner
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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 02:59

total area; 20*24*2 ; 960
available 1200 ;
∆
1200-960 /1200 = 20%
IMO D

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 03:05

1

Kudos

For 1200 cubic feet volume, height "\(h\)" that can be filled is
--> \(20*24*h = 1200\)
--> \(h = 2.5\) feet

Actual raised = 2

% more available = \(\frac{2.5 - 2}{2}*100 = 0.5*50 = 25\)

Option C

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exc4libur

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 04:17

1

Kudos

Quote:

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

initial volume: 20*24*1=480ft^3
final volume: 20*24*2=960ft^3
available sand / actual required sand: 1200/960-1=25%

Ans (C)

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madgmat2019

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 05:22

1

Kudos

from given .... 20*24*2 = 960 cubic feet.......
required = 1200......%increase = 240/960 = 25%

OA:C

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eakabuah

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 06:23

1

Kudos

Volume of sand required = 20*24*2 = 960cu. ft
Volume of sand available = 1200cu. ft
Excess sand = 1200-960 = 240cu. ft
Percentage of excess sand = 240/960 * 100%= 25%.

The answer is C.

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 11:19

1

Kudos

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

\(\frac{1200}{20*24*2} =\frac{5 }{4} = 1.25\)
25%

Answer C.
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lacktutor

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 17:00

1

Kudos

The actual sand (required) = 24*20*2= 960 cubic feet
—> 1200 cubic feet availabel

960 —100%
1200 —x
—> \(x\)=\(\frac{1200*100}{960}= \frac{1000}{8}=125\)

125 —100 = 25% (greater than the actual sand which is required)

The answer is C.

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joohwangie

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 18:30

1

Kudos

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?
100% = 20x24x2=960
1200=x/100 * 960
125%
therefore 25% greater
A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

C

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freedom128

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 19:09

1

Kudos

Sands required = 20*24*2 = 960 ft^3.
% excess = (1200-960)/960 *100% = 25%

FINAL ANSWER IS (C)

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amitahlawat06

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Joined: 14 Jul 2018

Posts: 20

Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 19:30

1

Kudos

25% is the answer

required = 20*24*2 =960
available = 1200 extra = 240
x% extra = 24000/960 = 25%

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ostrick5465

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 21:16

1

Kudos

\(\frac{1200}{20*24*2} * 100% \) =125%

=> Choice C 25%
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Jawad001

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

22 Jan 2020, 23:19

1

Kudos

After the floor of the rectangular park rises by 2 feet,
The length of park = 20 feet and
The wide of the park = 24 feet.

Before the floor of the rectangular park rises by 2 feet,
The length of park = 20-4 = 16 feet and
The wide of the park = 24- 4 = 20 feet.

20 by 24 feet to be filled with 1200 cubic feet of sand
16 by 20 feet to be filled with 1200*16*20/20*24 =800 cubic feet of sand

Percentage increased by 400/800 = 50%(A)

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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

24 Jan 2020, 10:21

1

Kudos

Expert Reply

Bunuel wrote:

Competition Mode Question

A rectangular park which is 20 feet long and 24 feet wide is to be filled with sand so that the floor of the rectangular park rises by 2 feet. If 1200 cubic feet of sand is available for this purpose, by what percentage is it greater than the actual sand which is required?

A. 50%
B. 40%
C. 25%
D. 20%
E. 10%

The amount of sand needed is 20 x 24 x 2 = 960 cubic feet. So 1200 is the following percent greater than 960:

(1200 - 960)/960 x 100 = 25%

Answer: C
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Re: A rectangular park which is 20 feet long and 24 feet wide is to be fil [#permalink]

24 Jan 2020, 10:21

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A rectangular park which is 20 feet long and 24 feet wide is to be fil

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