Two solutions are made by adding Chemical Z to water. Solution A is 40

Question

Two solutions are made by adding Chemical Z to water. Solution A is 40% Chemical Z and Solution B is 80% Chemical Z. A chemist combines Solution A and Solution B to make a mixture. If x percent of the Chemical Z in the combined mixture comes from Solution A, and if y percent of the total volume of the mixture comes from Solution A, which of the following expresses x in terms of y ?

A. \(\frac{60 y}{80 - y}\)

B. \(\frac{100 y}{200 - y}\)

C. \(\frac{120 y}{200 - y}\)

D. \(\frac{200 y}{240 - y}\)

E. \(\frac{400 y}{800 - y}\)

A.  \frac{60 y}{80 - y}

B.  \frac{100 y}{200 - y}

C.  \frac{120 y}{200 - y}

D.  \frac{200 y}{240 - y}

E.  \frac{400 y}{800 - y}

Abhishekgmat87 · Accepted Answer

Lets us assume that both solution are 100 ml each. Quantity of Z in the mixture will be 40 + 80 or 120 ml. 
x = 40*100/120 = (100/3) %

y = 100* 100/200 or 50 %

Put y=50 in options, only option B gives x equal to (100/3) %

Option B

Locomotivated · Answer

Bunuel , is there some information missing in the question? The question does not state that both mixtures are mixed equally. Because I am unable to solve it w/o assuming both mixtures are of equal quantity.

Bunuel · Answer

We are told that y percent of the total volume of the final mixture comes from Solution A.

Two solutions are made by adding Chemical Z to water. Solution A is 40% Chemical Z and Solution B is 80% Chemical Z. A chemist combines Solution A and Solution B to make a mixture. If x percent of the Chemical Z in the combined mixture comes from Solution A, and if y percent of the total volume of the mixture comes from Solution A, which of the following expresses x in terms of y ?

A. \(\frac{60 y}{80 - y}\)

B. \(\frac{100 y}{200 - y}\)

C. \(\frac{120 y}{200 - y}\)

D. \(\frac{200 y}{240 - y}\)

E. \(\frac{400 y}{800 - y}\)

A.  \frac{60 y}{80 - y}

B.  \frac{100 y}{200 - y}

C.  \frac{120 y}{200 - y}

D.  \frac{200 y}{240 - y}

E.  \frac{400 y}{800 - y}

Since y percent of the total volume of the mixture comes from Solution A, then 100 - y percent of the total volume of the mixture comes from Solution B.

1 liter of the final mixture would therefore contain 0.4y liters of Chemical Z from Solution A and 0.8(100 - y) liters of Chemical Z from Solution B. The total volume of Chemical Z would be 0.4y + 0.8(100 - y) = 80 - 0.4y liters.

Since x percent of the Chemical Z in the combined mixture comes from Solution A,  x = \frac{0.4y}{80 - 0.4y}*100 . Simplifying the fraction by dividing the numerator and denominator by 0.4 gives:  x = \frac{y}{200 - y}*100 , resulting in  x = \frac{100y}{200 - y} .

Answer: B.

Hope it's clear.

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Two solutions are made by adding Chemical Z to water. Solution A is 40

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Two solutions are made by adding Chemical Z to water. Solution A is 40

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