Explanation

This is an inverse-variation problem of the form y = k/√x. Substituting the given pair, 36 = k/√36 = k/6, so the constant of variation is k = 216. Setting y = 54 gives 54 = 216/√x, i.e. √x = 216/54 = 4, and squaring yields x = 16. Hence option (c). The distractors 27 and 8 arise from assuming y varies inversely with x itself or with x² instead of √x, and 54 ignores the variation entirely.