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During a two-year period, the water level in a lake decreased by 20 pe

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During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 10 May 2017, 02:37
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During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w

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Re: During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 10 May 2017, 03:06
Initial level = w
After the 1st year, water level reduces by 20%. Hence, the resulting water level would be 0.8w
After the 2nd year, the water level increased by 10%. Hence, the resultant water level would be 1.1*0.8w= 0.88w
Hence, Option D should be the correct answer.
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During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 10 May 2017, 08:45
Bunuel wrote:
During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w


Decrease by 20% [1-.20] = .80
Increase by 10% = [1+.10] 1.10

(.8)(1.1) = .88

Multiply that product by original value, w ==> .88w

Answer D
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Re: During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 12 May 2017, 13:40
Bunuel wrote:
During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w


We are given that the lake began at a level of w feet and that the level decreased 20% and then increased 10%. So the ending level is:

w x 0.8 x 1.1 = 0.88w

Answer: D
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Re: During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 16 May 2017, 05:42
During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w

Water level = w
After first year water level decreased by 20% = 80% of w
After second year water level increased by 10% = 110% of 80% of w
Therefore water level by the end of period = \(\frac{110}{100}\) x \(\frac{80}{100}\) x w = \(\frac{88}{100}\) x w = 0.88w
Answer D...

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Re: During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 16 May 2017, 08:32
Bunuel wrote:
During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w


Let, initial water level be "w"

Water level after 1st year = \(80/100*w\) \(= 0.80w\)
Water level after 2nd year = \(\frac{0.80w*110}{100}\) \(= 0.88w\)

Thus, level of water in feet after 2nd year is 0.88w
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Re: During a two-year period, the water level in a lake decreased by 20 pe  [#permalink]

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New post 16 May 2017, 08:37
Bunuel wrote:
During a two-year period, the water level in a lake decreased by 20 percent by the end of the first year and increased by 10 percent by the end of the second year. If the lake began the period with a water level of w feet, what was the level, in feet, by the end of the period?

A. 1.2w
B. 1.1w
C. 0.9w
D. 0.88w
E. 0.8w


Initial water level = w feet.
at the end of first year = 0.8 w
at the end of 2nd year = 0.8 x 1.1 w = 0.88 w

Answer D

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