If 0.04 : 0.06 :: 0.06 : A.
$$\frac{0.04}{0.06}=\frac{0.06}{A}$$
$$\frac{\frac{4}{100}}{\frac{6}{100}}=\frac{\frac{6}{100}}{A}$$
$$\frac{100}{6}\times\frac{4}{100}=\frac{6}{100A}$$
$$\frac{1}{3}\times\frac{1}{1}=\frac{3}{100A}$$
$$100A\ =\ 9$$
$$A\ =\ \frac{9}{100}$$
Value of A = 0.09
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