Combined variation with square root in denominator – UGC NET Question

The given relation can be written as x = k·y/√z for some constant k. Using x = 18 when y = 6 and z = 9, we have 18 = k·6/3, so 18 = 2k and k = 9. For y = 8 and z = 4, we get x = 9·8/√4 = 72/2 = 36. Thus, the new value of x is 36.

Option A:
Option A, 16, might be obtained by incorrectly treating the dependence on z as inverse linear (y/z) and misapplying the parameter values, but it does not follow from x = k·y/√z with k = 9. Substituting y = 8 and z = 4 into the correct formula clearly yields 36, not 16.

Option B:
Option B, 24, could arise from ignoring the square root and computing x = 9·8/3, but that would contradict the original pair (18, 6, 9) if we required a single consistent formula. The condition involves √z explicitly, so 24 is not compatible with that relationship.

Option C:
Option C, 30, does not match any straightforward misinterpretation of the formula that still respects both data points. When we use the correct k = 9 and plug in y = 8 and z = 4, we obtain 36, so 30 cannot be reconciled with the algebraic model.

Option D:
Option D is correct because it uses the same constant of proportionality derived from the first situation and correctly applies the dependence on y and √z. The computation 9·8/2 = 36 strictly follows x = k·y/√z and satisfies both given data conditions.