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If grapes are 92% water and raisins are 20% water, then how

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If grapes are 92% water and raisins are 20% water, then how [#permalink]  02 Sep 2013, 09:59
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If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)

A. 25 pounds
B. 46 pounds
C. 92 pounds
D. 100 pounds
E. 146 pounds

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Though I could get this question right, I took more than 3 minutes. Is there any simpler way to solve this one?
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  03 Sep 2013, 04:18
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pavan2185 wrote:
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)

A. 25 pounds
B. 46 pounds
C. 92 pounds
D. 100 pounds
E. 146 pounds

Spoiler Alert :VeritasPrep Mock Test Question.

Though I could get this question right, I took more than 3 minutes. Is there any simpler way to solve this one?

Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*10 --> x = 100.

Similar questions to practice:
each-of-the-cucumbers-in-100-pounds-of-cucumbers-is-composed-102354.html
five-kilograms-of-oranges-contained-98-of-water-141401.html
fresh-dates-contain-90-water-while-dry-dates-contain-143245.html

Hope this helps.
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  26 Nov 2013, 00:46
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pavan2185 wrote:
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)

A. 25 pounds
B. 46 pounds
C. 92 pounds
D. 100 pounds
E. 146 pounds

Spoiler Alert :VeritasPrep Mock Test Question.

Though I could get this question right, I took more than 3 minutes. Is there any simpler way to solve this one?

Responding to a pm:
Actually, the best method for this question is the one given by Bunuel. I used the same method to give the explanation in the mock too. But you can use weighted average if you wish.

Raisins have 20% water. Water is 100% water. You mix these two to make grapes which has 92% water. (This is another way of saying you remove water from grapes to make raisins)
In what ratio will you mix them?

Wr/Ww = (Cw - Cavg)/(Cavg - Cr) = (100 - 92)/(92 - 20) = 8/72 = 1/9

So every 1 unit of raisin will be mixed with 9 units of water to give 10 units of grapes.
So 10 pounds of raisins will mix with 90 pounds of water to give 100 pounds of grapes.

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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  03 Apr 2014, 23:10
Bunuel wrote:
pavan2185 wrote:
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 10 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)

A. 25 pounds
B. 46 pounds
C. 92 pounds
D. 100 pounds
E. 146 pounds

Spoiler Alert :VeritasPrep Mock Test Question.

Though I could get this question right, I took more than 3 minutes. Is there any simpler way to solve this one?

Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*10 --> x = 100.

Similar questions to practice:
each-of-the-cucumbers-in-100-pounds-of-cucumbers-is-composed-102354.html
five-kilograms-of-oranges-contained-98-of-water-141401.html
fresh-dates-contain-90-water-while-dry-dates-contain-143245.html

Hope this helps.

(Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)

Had the above highlighted condition not mentioned, would 46 pounds be the answer.. ?
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  10 May 2015, 08:43
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  11 May 2015, 07:42
Expert's post
If 92 percent of grapes is water then 8 percent is the fruit. If 20 percent of raisins is water then 80 percent is fruit.

.08 (x pounds) = .8 (10 pounds)
x = 100 pounds
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  06 Jun 2015, 19:46
Hi I understand the solution given but why is the answer not 46 pounds? why can't one get the answer by proportionality? what is the flaw in my logic?Would appreciate an answer if possible.
Thanks so much.
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  06 Jun 2015, 20:39
sykhong wrote:
Hi I understand the solution given but why is the answer not 46 pounds? why can't one get the answer by proportionality? what is the flaw in my logic?Would appreciate an answer if possible.
Thanks so much.

Hi,
to look at the flaw , you will have to give your solution.
i think where you could be going wrong in proportionality is by reducing the non water portion too in same ratio. It is clearly given that the loss is only of water portion, so non water portion will remain the same....
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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  08 Jun 2015, 21:03
Expert's post
Hi sykhong,

Until you show your 'steps', we won't know exactly where you made your mistake. We CAN prove why 46 pounds is NOT the correct answer though....

IF....the grapes weighted 46 pounds total and those grapes were 92% water, then we'd have....

Total = 46 pounds
Water = .92(46) = 42.32 pounds
Not-Water = 3.68 pounds

The part that is NOT-WATER is key here, since that number does NOT change.

The raisins would ALSO contain those 3.68 pounds of not-water, which would represent 80% of the weight (since 20% of the raisins are water).

3.68 = .8(Total Weight)
3.68/.8 = Total Weight
4.6 pounds = Total weight of the raisins

However, the prompt tells us that the raisins are supposed to weigh 10 POUNDS, so the 4.6 pounds is clearly TOO LOW and the grapes must weigh MORE than 46 pounds.

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Re: If grapes are 92% water and raisins are 20% water, then how [#permalink]  10 Jun 2015, 22:33
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Presenting a slightly alternate approach:

Since the weight of water is the difference between raisins and grapes, let's calculate the weight of water in $$10$$ pounds of raisins and water's weight in raisins when they were grapes

Water in raisins
For $$10$$ pounds of raisins there is $$20$$% of water. Hence amount of water = $$20$$% of $$10 = 2$$ pounds.

Water in grapes before they evaporated
Let $$x$$ pounds be the amount of water that evaporated. So when the raisins were grapes,

Total weight of water = $$2 + x$$

Total weight of grapes = $$10 + x$$

When raisins were grapes, $$\frac{Weight of Water}{Weight of Grapes} = 92$$%

i.e. $$\frac{2 + x}{10 + x} = 0.92$$.

Solving for $$x$$ would give $$x = 90$$ pounds.

Hence total weight of 10 pounds of raisins when they were grapes = $$10 + 90 = 100$$ pounds

Hope this helps

Regards
Harsh
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Re: If grapes are 92% water and raisins are 20% water, then how   [#permalink] 10 Jun 2015, 22:33
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