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Let the total number of people in the group be $100.$

- The number of people who are young $ = 28 \% \; \text{of} \; 100 = \frac{28}{100} \times 100 = 28$
- The number of people who are old $ = 100 – 28 = 72$

Among $100$ people, $65$ are literate, then $35$ people should be illiterate.

The number of literate people who are young $ = 25 \% \; \text{of} \; 65 = \frac{25}{100} \times 65 = 16.25$

- The number of literate people who are old $ = 65 – 16.25 = 48.75$
- The number of illiterate people who are old $ = 72 – 48.75 = 23.25$

$\therefore$ The percentage of old people among the illiterates $ = \left(\frac{23.25}{35} \right) \times 100\% = 66.42 \% \simeq 66\%.$

Correct Answer $: \text{C}$