Correct Option (B)

Let the two-digit natural number be represented as 10x + y, where x is the tens digit and y is the units digit. For a two-digit number, x must be an integer from 1 to 9, and y must be an integer from 0 to 9.

The number formed by reversing its digits is 10y + x.

According to the given information, the ratio of the original number to the reversed number is 4:7:

$\frac{10 x + y}{10 y + x} = \frac{4}{7}$

Cross-multiplying the equation yields:

$7 (10 x + y) = 4 (10 y + x)$

$70 x + 7 y = 40 y + 4 x$

Rearranging the terms to isolate x and y:

$70 x - 4 x = 40 y - 7 y$

$66 x = 33 y$

Dividing both sides by 33 gives the relationship between x and y:

$x = \frac{33}{66} y$

$x = \frac{1}{2} y$

Since x and y are digits, and x must be a non-zero integer (1-9), y must be an even integer from 2 to 8 to ensure x is an integer and within the valid range (1-4).

The possible pairs (x, y) that satisfy this condition are:

If y = 2, then x = (1/2) * 2 = 1. The number is 12.
If y = 4, then x = (1/2) * 4 = 2. The number is 24.
If y = 6, then x = (1/2) * 6 = 3. The number is 36.
If y = 8, then x = (1/2) * 8 = 4. The number is 48.

There are exactly four such pairs of two-digit numbers that satisfy the given condition.

Incorrect Options:

Options A (5), C (3), and D (2) are incorrect because the mathematical derivation and subsequent enumeration of valid digit pairs demonstrate that there are precisely four such numbers, not five, three, or two.