The sum of deviations of 'n' observations about 25 is 25 and sum of deviations of the same 'n' observations about 35 is -15. Then the arithmetic mean of the observations is

The sum of deviations of $n$ observations about a number $a$ means $\sum x_i - na$.

From the given conditions:

$\sum x_i - 25n = 25 \quad \cdots (1)$

$\sum x_i - 35n = -15 \quad \cdots (2)$

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Subtracting equation $(2)$ from equation $(1)$:

$(\sum x_i - 25n) - (\sum x_i - 35n) = 25 - (-15)$

$10n = 40$

$n = 4$

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Substituting $n = 4$ in equation $(1)$:

$\sum x_i = 25 + 25(4)$

$\sum x_i = 125$

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Mean $= \dfrac{\sum x_i}{n}$

$= \dfrac{125}{4}$

$= 31.25$

Since $31.25$ does not match any of the given options, the answer is None of these.