The mean of 5 observations is 60, mean of 10 observations is 30, and mean of 15 observations is 20; then mean of all the 30 observations is:

The correct answer is (c).

The total of the 30 observations is $5 \times 60 + 10 \times 30 + 15 \times 20 = 500$. The mean of all the 30 observations is therefore $\frac{500}{30} = 25$.

Option (a) is incorrect because $40$ is not the mean of any of the groups of 5, 10, or 15 observations.

Option (b) is incorrect because $30$ is the mean of the group of 10 observations, but it is not the mean of all the 30 observations.

Option (d) is incorrect because $20$ is the mean of the group of 15 observations, but it is not the mean of all the 30 observations.