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There are x number of apples in a bin. Susan takes 40 percent of the a

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There are x number of apples in a bin. Susan takes 40 percent of the a [#permalink]

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New post 11 Jan 2018, 20:52
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There are x number of apples in a bin. Susan takes 40 percent of the apples out of the bin. Later, she returns some apples so that she now has only 10 percent of the apples. There are now 27 apples left in the bin. How many apples does Susan have?

A. 3
B. 4
C. 9
D. 12
E. 30
[Reveal] Spoiler: OA

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There are x number of apples in a bin. Susan takes 40 percent of the a [#permalink]

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New post 12 Jan 2018, 09:33
Bunuel wrote:
There are x number of apples in a bin. Susan takes 40 percent of the apples out of the bin. Later, she returns some apples so that she now has only 10 percent of the apples. There are now 27 apples left in the bin. How many apples does Susan have?

A. 3
B. 4
C. 9
D. 12
E. 30

If you catch the logic at the end, the first part of this question, where Susan takes 40 percent of the apples and puts some back, is irrelevant as far as computing goes. We are given the result of what would be that computation.

We do not have a counting number for 40 percent.
We have no idea how many apples she took or left or put back.

We know that at the end, after taking and returning some, she has 10 percent of the apples originally in the bin.
That means the other 90 percent of the original apples are: in the bin.
And at the end, there are 27 apples in the bin.

Let \(A\) = original # of apples in the bin
\(27 = .90A\)
\(A = \frac{27}{(\frac{9}{10})}=(27*\frac{10}{9})= 30\)

Susan has 10 percent of the original apples:
(.10)(30) = 3 apples

Answer A
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Re: There are x number of apples in a bin. Susan takes 40 percent of the a [#permalink]

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New post 12 Jan 2018, 12:33
Bunuel wrote:
There are x number of apples in a bin. Susan takes 40 percent of the apples out of the bin. Later, she returns some apples so that she now has only 10 percent of the apples. There are now 27 apples left in the bin. How many apples does Susan have?

A. 3
B. 4
C. 9
D. 12
E. 30


Susan takes 40% of the apples from the bin. Hence, the bin which first had x apples
will not have 0.6x of the apples.

After sometime, she returns some apples such that she has only 10% of the apples.
As she would have returned 0.3x of the apples, the bin has 0.6x+0.3x = 0.9x of the
apples, which is 27. Hence, the total number of apples will be \(x = \frac{27}{0.9} = 30\)

Therefore, the number of apples that Susan has will be 0.1x or 3(Option A)

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Re: There are x number of apples in a bin. Susan takes 40 percent of the a   [#permalink] 12 Jan 2018, 12:33
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