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16 Sep 2014, 01:24
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Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as the result, a 40% solution of acid was obtained, what part of the original solution was replaced?
A. \(\frac{1}{5}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{4}{5}\)
A. \(\frac{1}{5}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{4}{5}\)
16 Sep 2014, 01:24
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Official Solution:
Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as the result, a 40% solution of acid was obtained, what part of the original solution was replaced?
A. \(\frac{1}{5}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{4}{5}\)
Since the concentration of acid in the resulting solution (40%) is the average of 50% and 30%, exactly half of the original solution was replaced.
Alternatively, you can do the following, say \(x\) part of the original solution was replaced, then: \((1-x)*0.5+x*0.3=1*0.4\), which gives \(x=\frac{1}{2}\).
Answer: C
Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as the result, a 40% solution of acid was obtained, what part of the original solution was replaced?
A. \(\frac{1}{5}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{4}\)
E. \(\frac{4}{5}\)
Since the concentration of acid in the resulting solution (40%) is the average of 50% and 30%, exactly half of the original solution was replaced.
Alternatively, you can do the following, say \(x\) part of the original solution was replaced, then: \((1-x)*0.5+x*0.3=1*0.4\), which gives \(x=\frac{1}{2}\).
Answer: C
General Discussion
