I have to agree with your answer.
Assuming, as you seem to have done, the R1 = R2 you need to charge to 1/2, which takes ln(2) time constants (0.693).
C=200µF and R=10000 gives a time constant of 2 seconds, so doesn't work with R1 = R2, but does work with a different ratio, so I can't disagree with their answer either.