**Solution:**

Let's assume the original weight of the diamond is W grams and its original value is V rupees.

According to the given information, the value of a diamond varies directly as the square of its weight. This can be expressed as:

V ∝ W^2

Now, let's consider the division of the diamond into two pieces in the ratio of 4:6. This means that the weight of the first piece is 4x and the weight of the second piece is 6x, where x is a common factor.

The total weight of the diamond is given by:

W = 4x + 6x = 10x

Now, let's calculate the value of each piece of the diamond.

According to the direct variation relationship, if the weight of the diamond is W grams, then its value is V rupees. So, if the weight of the first piece is 4x grams, then its value can be calculated as:

V1 ∝ (4x)^2 = 16x^2

Similarly, if the weight of the second piece is 6x grams, then its value can be calculated as:

V2 ∝ (6x)^2 = 36x^2

Since the total value of the diamond is Rs 10,000, we can write the equation as:

V1 + V2 = 10,000

Substituting the values of V1 and V2, we get:

16x^2 + 36x^2 = 10,000

52x^2 = 10,000

Dividing both sides of the equation by 52, we get:

x^2 = 192.3077

Taking the square root of both sides, we get:

x ≈ 13.88

Now, let's calculate the weight of each piece:

Weight of the first piece = 4x ≈ 4 * 13.88 ≈ 55.52 grams
Weight of the second piece = 6x ≈ 6 * 13.88 ≈ 83.28 grams

Now, let's calculate the value of each piece:

Value of the first piece = 16x^2 ≈ 16 * (13.88)^2 ≈ 3169.14 rupees
Value of the second piece = 36x^2 ≈ 36 * (13.88)^2 ≈ 7130.86 rupees

The total value of the diamond after division is:

Value = Value of the first piece + Value of the second piece
= 3169.14 + 7130.86
≈ 10,300 rupees

The loss in value can be calculated as:

Loss in value = Original value - New value
= 10,000 - 10,300
= -300 rupees

The loss in value as a percentage of the original value can be calculated as:

Loss percentage = (Loss in value / Original value) * 100
= (-300 / 10,000) * 100
≈ -3%

Since the loss percentage is negative, we take the absolute value to get the positive loss percentage:

Loss percentage ≈ 3%

Therefore, the loss in value is approximately 3%, which is closest to option B (48%).