Question
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: Option D
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5% of A + 4% of B = (6% of A + 8% of B)\(\frac{2}{3}\)
= \(\frac{5}{100}A + \frac{5}{100}B = \frac{2}{3}\left(\frac{6}{100}A + \frac{8}{100}B\right)\)
= \(\frac{1}{100}A +\frac{1}{100}B =\frac{1}{25}A + \frac{1}{75}B\)
= \(\left(\frac{1}{20}-\frac{1}{25}\right)A =\left(\frac{4}{75}- \frac{1}{25}\right)B\)
= \(\frac{1}{100}A =\frac{1}{75}B\)
\(\frac{A}{B} =\frac{100}{75}=\frac{4}{3 }.\)
So, Required ratio = 4:3.
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