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% by weight problem

by prachi18oct » Fri Jul 04, 2014 4:13 am
If grapes are 92% water and raisins are 20% water by weight, 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

Please explain the solution!!
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by GMATGuruNY » Fri Jul 04, 2014 6:18 am
prachi18oct wrote:If grapes are 92% water and raisins are 20% water by weight, 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
Since raisins are 20% water, the 10 pounds of raisins are composed of 2 pounds of water and 8 pounds of other stuff.
Since grapes are 92% water, the 8 pounds of other stuff must constitute 8% of the grapes:
8 = (8/100)x
x = 800/8 = 100.

The correct answer is D.
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by GMATinsight » Fri Jul 04, 2014 8:07 am
If grapes are 92% water and raisins are 20% water by weight, 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
Suppose that the grapes were 100x pounds

Then water in the grapes = 92x pounds
and Pulp (stuff other than water) in the grapes = 100x-92x = 8x pounds

From Grapes to Raisin, only water evaporates which means the Pulp (stuff other than water) remains same after the conversion of grapes into raisins

Which means 8x = 80%of raising [as Raisin have 20 water and 80% other stuff]
therefore, 100% weight of Raisin = 10x = 10 pounds 9Given)

therefore x=1

therefore weight of Grapes = 100x = [spoiler]100 Pounds ANSWER OPTION D[/spoiler]
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