Discussion
Two numbers \(A\) and \(B\) are such that the sum of 5 % of \(A\) and 4 % of \(B \) is two-third of the sum of 6 % of \(A\) and 8 % of \(B. \) Find the ratio of \(A:B\)
Answer: D
5 % of \(A\) + 4% of \(B\) \(= \frac{2}{3}\) (6% of \(A + 8\)% of \(B\))
\(\Rightarrow \frac{5}{100}A + \frac{4}{100}B = \frac{2}{3}(\frac{6}{100}A + \frac{8}{100}B)\)
\(\Rightarrow \frac{1}{20}A + \frac{1}{25}B = \frac{1}{25}A + \frac{4}{75}B\)
\(\Rightarrow (\frac{1}{20} - \frac{1}{25})A = (\frac{4}{75} - \frac{1}{25})B\)
\(\Rightarrow \frac{1}{100}A = \frac{1}{75}B\)
\(\frac{A}{B} = \frac{100}{75} = \frac{4}{3}\)
\(\therefore Required ratio = 4: 3\)
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