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16 Sep 2014, 01:02
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The ratio of \(a\) to \(b\) is 1 to 2. If \(a\) is increased by \(x\%\) and \(b\) is decreased by \(\frac{x}{2}\%\), where \(x\neq 0\), which of the following represents the new ratio of \(a\) to \(b\)?
A. \(\frac{100 + x}{200 - x}\)
B. \(\frac{1 + \frac{x}{100} }{1 - \frac{x}{200} }\)
C. \(\frac{x + 1}{2x + 2}\)
D. \(\frac{2x + 1}{200 - x}\)
E. \(\frac{200 + x}{1 - x}\)
A. \(\frac{100 + x}{200 - x}\)
B. \(\frac{1 + \frac{x}{100} }{1 - \frac{x}{200} }\)
C. \(\frac{x + 1}{2x + 2}\)
D. \(\frac{2x + 1}{200 - x}\)
E. \(\frac{200 + x}{1 - x}\)
16 Sep 2014, 01:02
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Official Solution:
The ratio of \(a\) to \(b\) is 1 to 2. If \(a\) is increased by \(x\%\) and \(b\) is decreased by \(\frac{x}{2}\%\), where \(x\neq 0\), which of the following represents the new ratio of \(a\) to \(b\)?
A. \(\frac{100 + x}{200 - x}\)
B. \(\frac{1 + \frac{x}{100} }{1 - \frac{x}{200} }\)
C. \(\frac{x + 1}{2x + 2}\)
D. \(\frac{2x + 1}{200 - x}\)
E. \(\frac{200 + x}{1 - x}\)
The new ratio is:
\(\frac{1(1 + \frac{x}{100})}{2(1 - \frac{x}{200})} = \)
\(=\frac{1 + \frac{x}{100} }{2 - \frac{x}{100} } =\)
\(=\frac{\frac{100 + x}{100} }{\frac{200 - x}{100} } =\)
\(=\frac{100 + x}{100}* \frac{100}{200 - x} =\)
\(= \frac{100 + x}{200 - x}\).
Answer: A
The ratio of \(a\) to \(b\) is 1 to 2. If \(a\) is increased by \(x\%\) and \(b\) is decreased by \(\frac{x}{2}\%\), where \(x\neq 0\), which of the following represents the new ratio of \(a\) to \(b\)?
A. \(\frac{100 + x}{200 - x}\)
B. \(\frac{1 + \frac{x}{100} }{1 - \frac{x}{200} }\)
C. \(\frac{x + 1}{2x + 2}\)
D. \(\frac{2x + 1}{200 - x}\)
E. \(\frac{200 + x}{1 - x}\)
The new ratio is:
\(\frac{1(1 + \frac{x}{100})}{2(1 - \frac{x}{200})} = \)
\(=\frac{1 + \frac{x}{100} }{2 - \frac{x}{100} } =\)
\(=\frac{\frac{100 + x}{100} }{\frac{200 - x}{100} } =\)
\(=\frac{100 + x}{100}* \frac{100}{200 - x} =\)
\(= \frac{100 + x}{200 - x}\).
Answer: A
09 Feb 2016, 18:32
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Alternate approach :
Let A and B be 100 and 200. Ratio 1:2. Now think, x% of 100 is actually x/2% of 200. 10% of 100 ( which is 10 in this case) is 5% of 200. So, basically we are adding and subtracting the same amount from numerator and denominator. Option A does exactly that (100+x)/(200-x).
Thus, answer A.
Let A and B be 100 and 200. Ratio 1:2. Now think, x% of 100 is actually x/2% of 200. 10% of 100 ( which is 10 in this case) is 5% of 200. So, basically we are adding and subtracting the same amount from numerator and denominator. Option A does exactly that (100+x)/(200-x).
Thus, answer A.
