A set of letters is followed by the product of their alphabetical positions.
ACE : 15 :: BDF : ?

The correct option is 48.

Step-by-Step Explanation:

The problem gives us a pattern where a set of letters is related to a number representing the product of their alphabetical positions.

1. Analyze the first pair (ACE : 15):

First, find the alphabetical positions of each letter in ACE:

• Position of A = 1

• Position of C = 3

• Position of E = 5

Now, calculate the product of these positions:

$1\times 3\times 5=15$

This matches the given relationship (ACE : 15).

2. Apply the same rule to the second set of letters (BDF):

Determine the alphabetical positions of each letter in BDF:

• Position of B = 2

• Position of D = 4

• Position of F = 6

Now, multiply these numerical values together:

$2\times 4\times 6=48$

Therefore, BDF : 48.