DSBO Company produces Z units of output at a total cost of Rs. R, where $$R=\frac{1}{10}Z^{3}-5Z^{2}+10Z+5$$ At what level of output will the average variable cost attain its minimum?

$$Z$$ is the number of items produced by the company.
Total cost, $$R=\frac{1}{10}Z^{3}-5Z^{2}+10Z+5$$
As we can see, the term '5' does not vary with the number of quantities produced. Therefore, 5 is the fixed cost. 
Variable cost = $$\frac{1}{10}Z^{3}-5Z^{2}+10Z$$
Average variable cost = Total variable cost/ number of quantities.
Average variable cost =$$\frac{1}{10}Z^{2}-5Z+10$$
=$$\frac{Z^2-50Z+100}{10}$$
=$$\frac{(Z^2-50Z+625)- 525}{10}$$
=$$\frac{(Z-25)^2-525}{10}$$
As we can see, the least value of the expression will be obtained at $$Z=25$$
Therefore, option C is the right answer.