Given: $2\cos a - 8\sin a + 10$ and $4\sin a - \cos a + 5$, where $\tan a = 0.25$

We know that $\tan a = \frac{\sin a}{\cos a} = 0.25$

So, $\sin a = 0.25 \cos a$

Substituting this value in the denominator of the given expression, we get:

$4\sin a - \cos a + 5 = 4(0.25\cos a) - \cos a + 5 = 2\cos a + 5$

Similarly, substituting the value of $\sin a$ in the numerator, we get:

$2\cos a - 8\sin a + 10 = 2\cos a - 8(0.25\cos a) + 10 = 2\cos a - 2\cos a + 10 = 10$

So, the expression simplifies to:

$\frac{10}{2\cos a + 5}$

To find the value of $\cos a$, we can use the fact that $\tan a = \frac{\sin a}{\cos a} = 0.25$

Squaring both sides, we get:

$\tan^2 a = \frac{\sin^2 a}{\cos^2 a} = 0.0625$

$\frac{1 - \cos^2 a}{\cos^2 a} = 0.0625$

$1 - \cos^2 a = 0.0625\cos^2 a$

$1 = 1.0625\cos^2 a$

$\cos^2 a = \frac{1}{1.0625} = 0.941$

Taking the square root, we get:

$\cos a \approx 0.969$

Substituting this value in the expression we simplified earlier, we get:

$\frac{10}{2\times 0.969 + 5} \approx 1.116$

Therefore, the value of the given expression is approximately 1.116.