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A beaker contains 100 milligrams of a solution of salt and water that
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04 Feb 2021, 08:29
04 Feb 2021, 08:29
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A beaker contains 100 milligrams of a solution of salt and water that is x% salt by weight such that \(x < 90\). If the water evaporates at a rate of \(y\) milligrams per hour, how many hours will it take for the concentration of salt to reach \((x + 10)\)%, in terms of \(x\) and \(y\)?
(A) \(x^x y^y=\frac{24^3}{2}\)
(B) \(\frac{1000 + 99x}{xy+10y}\)
(C) \(\frac{100y+100xy}{x+10}\)
(D) \(\frac{1000}{xy+10y}\)
(E) \(\frac{\sqrt{x+y}}{2}\)
(A) \(x^x y^y=\frac{24^3}{2}\)
(B) \(\frac{1000 + 99x}{xy+10y}\)
(C) \(\frac{100y+100xy}{x+10}\)
(D) \(\frac{1000}{xy+10y}\)
(E) \(\frac{\sqrt{x+y}}{2}\)
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A beaker contains 100 milligrams of a solution of salt and water that
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08 Feb 2021, 00:37
08 Feb 2021, 00:37
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GeminiHeat wrote:
A beaker contains 100 milligrams of a solution of salt and water that is x% salt by weight such that \(x < 90\). If the water evaporates at a rate of \(y\) milligrams per hour, how many hours will it take for the concentration of salt to reach \((x + 10)\)%, in terms of \(x\) and \(y\)?
(A) \(x^x y^y=\frac{24^3}{2}\)
(B) \(\frac{1000 + 99x}{xy+10y}\)
(C) \(\frac{100y+100xy}{x+10}\)
(D) \(\frac{1000}{xy+10y}\)
(E) \(\frac{\sqrt{x+y}}{2}\)
(A) \(x^x y^y=\frac{24^3}{2}\)
(B) \(\frac{1000 + 99x}{xy+10y}\)
(C) \(\frac{100y+100xy}{x+10}\)
(D) \(\frac{1000}{xy+10y}\)
(E) \(\frac{\sqrt{x+y}}{2}\)
Salt = X mg
Water = (100 - X) mg
Rate of evaporation = Y mg/hour
Time required to evaporate (100 - X) mg of water = (100 - X) / Y
As per the question, the new concentration of salt = (X + 10)% of total
Let, the time required to evaporate (X + 10)% of salt = T hours
NOTE: Since the water is evaporation at a rate of Y mg/hour, so in time T, YT mg of water will evaporate. Therefore, the Total amount in the beaker would now change to (100 - YT) mg
So, Salt = (X + 10) / 100 = X / (100 - YT)
100X = (X + 10)(100 - YT)
YT (X + 10) = 100(X + 10) - 100X
T = 1000 / (XY + 10Y)
Hence, option D
gmatclubot
A beaker contains 100 milligrams of a solution of salt and water that [#permalink]
08 Feb 2021, 00:37
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