Puzzles with Roman numerals

This passage is taken from Number Stories of Long Ago, by David Eugene Smith:

Titus liked to puzzle a chum of his named Caius, and one day he asked him this question : " What is the number that becomes one more when one is taken away from it ?"

"Your head," replied Caius, "must be just plain wood."

But when Titus wrote IX on the stone pavement and said to Caius, "Now take away the I and tell me what you have left,"Caius saw that the wooden head had something in it after all.

Then Caius, remarking that he could think of many other numbers that would answer just as well, asked this question: "What is the number that becomes ten more when ten is taken away ? "Titus then asked Caius if he knew that half of nine was four, and Caius replied that he must be dreaming. But Titus pointed again to IX and asked Caius to take the upper half of it and see if it was not IV. Then Caius said that he could show that half of twelve was seven.

"That is nothing," said Titus; "half of thirteen is eight."

"That is easy," said Caius ; "but can you take one hundred from four hundred and
have five hundred left ?"