A jar contains one quarter red jelly beans and three quarters blue jelly beans. If Chris removes three quarters of the red jelly beans and one quarter of the blue jelly beans, what percent of the jelly beans remaining in the jar will be
red?
1. **Determine the initial proportions of jelly beans in the jar:**
   - The jar contains one quarter red jelly beans and three quarters blue jelly beans.
   - Let the total number of jelly beans in the jar be \( N \).
   - The number of red jelly beans is \( \frac{1}{4}N \).
   - The number of blue jelly beans is \( \frac{3}{4}N \).

2. **Calculate the number of jelly beans removed by Chris:**
   - Chris removes three quarters of the red jelly beans:
     \[
     \text{Red jelly beans removed} = \frac{3}{4} \times \frac{1}{4}N = \frac{3}{16}N
     \]
   - Chris removes one quarter of the blue jelly beans:
     \[
     \text{Blue jelly beans removed} = \frac{1}{4} \times \frac{3}{4}N = \frac{3}{16}N
     \]

3. **Calculate the number of jelly beans remaining in the jar:**
   - The number of red jelly beans remaining:
     \[
     \text{Red jelly beans remaining} = \frac{1}{4}N - \frac{3}{16}N = \frac{4}{16}N - \frac{3}{16}N = \frac{1}{16}N
     \]
   - The number of blue jelly beans remaining:
     \[
     \text{Blue jelly beans remaining} = \frac{3}{4}N - \frac{3}{16}N = \frac{12}{16}N - \frac{3}{16}N = \frac{9}{16}N
     \]

4. **Calculate the total number of jelly beans remaining in the jar:**
   \[
   \text{Total jelly beans remaining} = \frac{1}{16}N + \frac{9}{16}N = \frac{10}{16}N = \frac{5}{8}N
   \]

5. **Determine the percentage of the remaining jelly beans that are red:**
   - The fraction of the remaining jelly beans that are red:
     \[
     \text{Fraction of red jelly beans} = \frac{\frac{1}{16}N}{\frac{5}{8}N} = \frac{1}{16} \div \frac{5}{8} = \frac{1}{16} \times \frac{8}{5} = \frac{8}{80} = \frac{1}{10}
     \]
   - Convert the fraction to a percentage:
     \[
     \text{Percentage of red jelly beans} = \frac{1}{10} \times 100\% = 10\%
     \]

Conclusion:
The percentage of the jelly beans remaining in the jar that are red is \( \boxed{10\%} \).