Step 1: Understanding the Question.
We must find the maximum amount the family can save in a month, including the PF amount, if they have no children and so spend nothing on children's education.
Step 2: Key Formula or Approach.
PF is money that never reaches the family's hand in the first place, so it already counts as a form of saving. On top of that, whatever share of the net income was set aside for children's education is freed up if there are no children, and that amount adds to the savings too.
Step 3: Detailed Explanation.
The PF deduction is
\[
0.10 \times 5000 = 500
\]
The net income, as found earlier, is Rs. 5,500, and all five expenditure percentages (food, rent, entertainment, education, other expenses) together add up to exactly 100 percent of this net income, which means that in the normal case nothing is left over as extra savings from take-home pay.
Children's education is budgeted at 25 percent of the net income:
\[
0.25 \times 5500 = 1375
\]
If there are no children, this Rs. 1,375 is never spent, so it becomes additional savings.
The total maximum savings, including the PF that was already set aside, is
\[
500 + 1375 = 1875
\]
Step 4: Final Answer.
The family can save at most Rs. 1,875 a month, so option (c) is correct.
\[ \boxed{Rs.\ 1875} \]