Select the pair which is related to each other in the same way as the following –
72:27

To find the pair that is related in the same way as the given pair 72:27, let's analyze the relationship between the two numbers in the base pair.

First, let's find the difference between the two numbers:
72 - 27 = 45

Let's also look at the sum of the digits of the first number:
7 + 2 = 9
And the sum of the digits of the second number:
2 + 7 = 9

We notice that both numbers in the pair 72:27 have a digit sum of 9. Furthermore, the digits of 27 are the reverse of the digits of 72. Let's see if this logic applies to the options, or if we need a different arithmetic relation.

Let's analyze the options to find a similar logic:

1. 27:45
Difference: 45 - 27 = 18
Digit sum of 27: 2 + 7 = 9
Digit sum of 45: 4 + 5 = 9
Although digit sums are equal, the pattern of reversing digits does not apply, and the difference is 18 instead of 45.

2. 56:33
Let's analyze the mathematical relationship in the given pair 72:27 again:
72 = 9 × 8
27 = 9 × 3
Here, both numbers are multiples of 9, with the multipliers being 8 and 3.
Let's see if we can find a general rule:
If the first number is $x$ and the second is $y$:
The difference is $72-27=45$.
Another logic is the operation on digits:
For 72: (7 + 2) = 9, and 9 × 3 = 27 (the second number).
Let's check if this rule "Sum of digits of first number multiplied by 3 equals the second number" works for any option:
- For 56:33: Sum of digits of 56 is 5 + 6 = 11. If we multiply this sum by 3, we get: 11 × 3 = 33, which is exactly the second number!

Let's verify this logic:
Given pair: 72:27
Sum of digits of 72 = 7 + 2 = 9
Multiplying the sum by 3: 9 × 3 = 27 (which is the second number).

Applying the same logic to the pair 56:33:
Sum of digits of 56 = 5 + 6 = 11
Multiplying the sum by 3: 11 × 3 = 33 (which is the second number).

This relationship holds true. Therefore, 56:33 is the correct related pair.