gsingh0711 wrote:

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) 20%

C) 10%

D) 40%

E) 25%

The hitch in this question is translating the highlighted portion. "IT" = the available 1,200 cubic feet of sand

(1) Volumes of sand: actually needed vs. available

The floor of flat rectangular park rises 2 feet -- in other words, the flat rectangle becomes a rectangular box

Actual volume of sand

needed = Volume of the rectangular box, \(V=l*w*h\)

\(l=24\) feet

\(w=20\) feet

\(h=2\) feet

Actually needed volume of sand: \(20*24*2=960\) cu ft

Available volume of sand: \(1,200\) cu ft

(2) Percent greater than?

By what percentage is AVAILABLE sand ("it") greater than volume of

actual sand

needed?

(Available) \(1,200\) is what percent greater than (actually needed) \(960\)?

Percent greater than = Percent change*

Percent change: \(\frac{New-Old}{Old}*100\)

\(\frac{1,200-960}{960}=\frac{240}{960}=\frac{1}{4}=(0.25*100)\)

\(=25\) percent

Answer E

Alternatively, percent greater than: \((\frac{NewValue}{OldValue}-1)=\) decimal % greater than

Subtract 1 to account for 100% of old value

\(\frac{1,200}{960}=1.25\), and \((1.25-1)=0.25\)

1,200 is 25 percent greater than 960

Answer E

"Old" = "Original." Another way to write the formula is \(\frac{Change}{Original}*100\). Almost always, the value after the word "than" is the Old/Original number.
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