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Mary decided to save a certain amount of her monthly salary each month

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Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 02:40
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Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?

(A) 1/2
(B) 2/3
(C) 1/4
(D) 4/5
(E) 5/6

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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 03:14
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Let Mary's monthly savings = S
Mary's monthly pay = P
Mary's monthly expenditure = P-S

Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month
12S = 3*(P-S)
=>4S = P-S
=> P = 5S

Mary's monthly expenditure = P-S = 5S-S = 4S

fraction of her salary that Mary spent each month = 4S / 5S = 4/5
Answer D
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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 03:50
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Bunuel wrote:
Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?

(A) 1/2
(B) 2/3
(C) 1/4
(D) 4/5
(E) 5/6



Hi,

Let the salary per month be y and expenditure be x..
If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, -- \(3(y-x) = 12x........y-x=4x......y=5x\)

fraction of salary spent = \(\frac{y-x}{y} = \frac{5x-x}{5x} =\frac{4x}{5x}= \frac{4}{5}\)..
D
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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 04:32
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Bunuel wrote:
Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?

(A) 1/2
(B) 2/3
(C) 1/4
(D) 4/5
(E) 5/6


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Quote:
Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month what should be the fraction of her salary that she spent each month?


Or, 12i - 12e = 3e
Or, 12i = 15e
Or, 5e = 4i
Or, e = 4i/5

Hence the correct answer will be (D)
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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 05:42
Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=3E=3(I-E)
=> 15S = 3I => Savings = 1/5
Hence Expenditure = 1-(1/5) = 4/5 Answer (D)
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A simpler way which helped me solve the problem in 15 sec.
Analyze the ans needs to be in the form = Expenditure / Income
Hence [3 times the numerator of the answer choices = 12 times the difference (Numerator - Denominator)]
So ..
(A) 1/2 => 3 x (1) = 12 x (2-1) ... Incorrect
(B) 2/3 => 3 x (2) = 12 x (3-2) ... Incorrect
(C) 1/4 => 3 x (1) = 12 x (4-1) ... Incorrect
(D) 4/5 => 3 x (4) = 12 x (5-4) ... Correct
(E) 5/6 => 3 x (5) = 12 x (6-5) ... Incorrect

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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 29 May 2016, 06:07
Savg.=Sal.-Spendg.

(here Savg., sal. and spendg. are monthly).

Therefore: 3 spendg. =12 savng.
solving==> 3 spendg.=12 sal. -12 spendg.
15 Spendg=12 Sal.
Spendg=4/5 *sal.

(D)
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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 16 Aug 2017, 21:09
Let assume her monthly salary is 100
Yearly income is 1200
Let she spend x per month. So total expenditure is 12x
Total saving is 3 times monthly expenditure i.e. 3x.
Total income is total savings + total expenditure = 12x+3x = 15x = 1200
so x = \(\frac{1200}{15}\) = 80
Thus fraction of expenditure per month = \(\frac{80}{100}\) =\(\frac{4}{5}\)
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Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 05 Oct 2018, 01:26
Let T be the amount spent and X be the total income. Thus, the amount saved = (X-T). The question asks us to find \(\frac{T}{X}\).

We can set up an equation:

\(12(X-T)=3T\)
\(12X-12T=3T\)
\(12X=15T\)
\(\frac{12}{15}=\frac{X}{T}\)
\(\frac{4}{5}=\frac{T}{X}\)

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Re: Mary decided to save a certain amount of her monthly salary each month  [#permalink]

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New post 07 Oct 2018, 18:23
Bunuel wrote:
Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?

(A) 1/2
(B) 2/3
(C) 1/4
(D) 4/5
(E) 5/6


We can let Mary’s monthly savings = n and monthly spending = p.

At the end of the year, her savings was 12n, which was 3 times what she spent per month, and thus:

12n = 3p

4n = p

Thus, the fraction that she spent each month was p/(p + n) = 4n/(4n + n) = 4/5.

Answer: D
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Re: Mary decided to save a certain amount of her monthly salary each month &nbs [#permalink] 07 Oct 2018, 18:23
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