Question

The value of \[{\rm{CDI}} + {\rm{V}} + {\rm{C}} + {\rm{X}}\] is equal to
A.506
B.401
C.406
D.516

Answer 1

Hint: Here, we will identify each of the roman numbers given in the question and represent it in the form of a normal number (as written in the Hindu-Arabic number system). Then we will add all the numbers. The sum will be our required solution.

Complete step-by-step answer:
In roman numerals, different symbols are used to represent different numbers. For example,
 I represents 1
V represents 5
X represents 10
L represents 50
C represents 100
D represents 500 and
M represents 1000.
If a symbol is written on the left side of another symbol, we have to subtract the symbol on the left from the symbol on the right to find the value of the roman number. For example
IV has symbol I on the left of symbol V so it is equivalent to 4. So, we can say
\[5 - 1 = 4\]
Similarly, IX represents 9.
If a symbol is written on the right side of another symbol, we have to add the symbol on the left with the symbol on the right to find the value of the roman number. For example
VI has symbol I on the right of symbol V so it is equivalent to 6. So, we can write
\[5 + 1 = 6\]
Similarly, XI represents 11.
So, CD will represent:
\[ \Rightarrow 500 - 100 = 400\]
And CDI will represent:
\[ \Rightarrow 400 + 1 = 401\]
We already know that V represents 5, C represents 100 and X represents 10. We will add all the numbers:
\[\begin{array}{l}{\rm{CDI}} + {\rm{V}} + {\rm{C}} + {\rm{X}} = 401 + 5 + 100 + 10\\ \Rightarrow {\rm{CDI}} + {\rm{V}} + {\rm{C}} + {\rm{X}} = 516\end{array}\]
$\therefore $ Option D is the correct option.

Note: Here we need to have the knowledge about the Roman numerals. Roman numerals are a type of numbers which originated in Rome and are represented with the help of letters. Also it is important to know the rule of subtraction and addition. However the rule of subtraction is only valid for numbers that are close to each other. For example, I (1) cannot be placed before L (50) or C (100) or D (500) or M (1000). So, 49 can’t be written as IL, it will be written as XLIX \[\left( {50 - 10} \right)\] and \[\left( {10 - 1} \right)\].