Solution
$$3^a = 5^b = 75^c = k$$
$$3 = k^{\frac{1}{a}}, 5 = k^{\frac{1}{b}}, 75 = k^{\frac{1}{c}}$$
$$75 = 3 \times 5^2$$
$$k^{\frac{1}{c}} = k^{\frac{1}{a}} \times k^{\frac{2}{b}}$$
$$\frac{1}{c} = \frac{1}{a} + \frac{2}{b}$$
$$c = \frac{ab}{2a + b}$$
$$c(2a + b) = ab$$
Hence the answer is option B
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