To solve this problem, we need to understand how the breaking of the stone affects its value and then calculate the percentage loss due to it being broken.

The stone breaks into four pieces with weights in the ratio 1:2:3:4. Let's denote the common factor of proportionality of these weights by \( x \). Therefore, the weights of the pieces are \( x \), \( 2x \), \( 3x \), and \( 4x \).

The value of a stone is proportional to the square of its weight. Thus, if the original weight of the stone is \( W \), the value of the stone before breaking is proportional to \( W^2 \).

First, calculate the total weight of the stone before and after breaking:

• The total weight before breaking is: \(W = (1+2+3+4)x = 10x\).

The value of the stone before breaking is proportional to \((10x)^2 = 100x^2\).

Now calculate the value of the stone after breaking:

• The value of the first piece is proportional to \( (x)^2 = x^2 \).
• The value of the second piece is proportional to \( (2x)^2 = 4x^2 \).
• The value of the third piece is proportional to \( (3x)^2 = 9x^2 \).
• The value of the fourth piece is proportional to \( (4x)^2 = 16x^2 \).

The total value of the stone after breaking is: \(x^2 + 4x^2 + 9x^2 + 16x^2 = 30x^2\).

To find the percentage loss in value, use the formula:

\(\text{Percentage Loss} = \left(\frac{\text{Original Value} - \text{New Value}}{\text{Original Value}}\right) \times 100%\)

Substitute the values we calculated:

\(\text{Percentage Loss} = \left(\frac{100x^2 - 30x^2}{100x^2}\right) \times 100%\)

\(\text{Percentage Loss} = \left(\frac{70x^2}{100x^2}\right) \times 100% = 70%\)

Thus, the percent loss in value incurred due to breaking is 70%.