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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5

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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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New post Updated on: 09 Jan 2013, 03:19
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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

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Originally posted by chiccufrazer1 on 08 Jan 2013, 13:08.
Last edited by Bunuel on 09 Jan 2013, 03:19, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A 7.5 litre mixture of water and sugar is 60%sugar.if 1.5 li  [#permalink]

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New post 08 Jan 2013, 13:23
multiply 7.5 by 10...so 75 Liters of solution which is 30 L Water and 45L Sugar

If you add 1.5x10 (15 L) of water the overall solution will contain 90L. Of that 90L 45L is water and 45 L is sugar.

Answer: B
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Re: A 7.5 litre mixture of water and sugar is 60%sugar.if 1.5 li  [#permalink]

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New post 08 Jan 2013, 13:32
Ya sambam ofcos the official answer is B.50 percent but am not satisified with how i got it..this is how i did it.if 7.5 =60% therefore 1.5 would equal 12.i decided to represent 1.5 as 1 part of water and hence in 7.5 i had 5 parts of water..the addition of water will made the new mixture to have 6 parts of water and a less percentage of sugar when i added 1.5 litres.. I said to myself that if 5 parts of water represent 60percent sugar then 6 parts will have to represent a small percentage of sugar i.e (5*60/6)%..thanks for making it clear to me!:-)

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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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New post 29 Dec 2017, 13:49
Top Contributor
chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68


ASIDE: We can eliminate C, D and E immediately (without performing any calculations).
Here's why: If we begin with a mixture that's 60% sugar and then we dilute it by adding water, the resulting mixture will have less than 60% sugar. So, eliminate C, D and E.

Okay, on to the solution.

7.5 liter mixture of water and sugar is 60% sugar.
60% of 7.5 liters is sugar
60% of 7.5 = 4.5, so the 4.5 mixture has 4.5 liters of sugar

1.5 liters of water is added
So, the volume of the new mixture is 9 liters.
Since no sugar was added, the volume of the sugar is still 4.5 liters

(4.5)/9 = 1/2 = 50%
So, the new mixture is [spoiler]50% sugar[/spoiler].
Answer: B


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A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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New post 29 Dec 2017, 16:31
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chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68
If you are used to weighted averages. . .

Water has 0.0 percent sugar, but it is being added

\(.6(7.5) + 0.0(1.5) = \frac{x}{100}(7.5 + 1.5)\)
Both sides * 100:
\(6(75) = 9x\)
\(450 = 9x\)
\(x = 50\) percent

Answer B
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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5  [#permalink]

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New post 31 Dec 2017, 11:31
chiccufrazer1 wrote:
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

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Initial ratio of Water and Sugar \(= 40: 60 = 2: 3\)

Thus, the amount of water \(= \frac{2}{(2+3)} * 7.5 = 3\) liters and the amount of sugar \(= \frac{3}{(2+3)} * 7.5 = 4.5\) liters

Water added \(= 1.5\) liters

Thus, total amount of water and sugar mixture \(= 7.5 + 1.5 = 9\) liters

Percentage of sugar \(= \frac{4.5}{9} = 50\) liters

Correct Answer: Option B


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Re: A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5   [#permalink] 31 Dec 2017, 11:31
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