(A) 12
Using the empirical relation: $3 \text{ Median} = \text{Mode} + 2\text{ Mean}$
Given: Mode − Median = 24, so Mode = Median + 24.
$$3\text{ Median} = (\text{Median} + 24) + 2\text{ Mean}$$
$$\text{Median} - \text{Mean} = 12$$
The key formula is the empirical relationship 3 Median = Mode + 2 Mean (from Chapter 13, Remarks). Rearranging gives Mode − Mean = 3(Median − Mean), and Mode − Median = 2(Median − Mean). So Median − Mean = (Mode − Median)/2 = 24/2 = 12. Remember this shortcut for MCQs.