Question

What is the value of $IX + XV + XX$?
A. $45$
B. $35$
C. $44$
D. $40$

Answer 1

Hint: In this question, we are given an expression in roman numbers and we are asked to find their sum. Start by converting the roman numbers into our regular numbers and then simply add them to find the answer.

Complete step-by-step answer:
We often get confused between the meaning of $IX$ and $XI$, or between any such roman number in which a smaller letter is placed before or after a bigger letter. Before solving the given expression, let’s clear the doubt in such a way that they become crystal clear.
Case 1:
When a bigger letter is placed before a smaller letter:
Let’s take an example of $XV$. In this, $V$ is a smaller letter as it represents $5$ and $X$ is a bigger letter as it represents $10$. If a smaller letter is placed after the bigger one, it is added to the bigger letter. In $XV$, $V$(smaller letter) is placed after$X$(bigger letter). Hence, it will be added.
$ \Rightarrow XV = 10 + 5 = 15$
Case 2:
When a smaller letter is placed before a bigger letter:
Let’s take an example of $IX$. In this, $I$ is a smaller letter as it represents $1$ and $X$ is a bigger letter as it represents $10$. If a smaller letter is placed before the bigger one, it is subtracted from the bigger letter. In $IX$, $I$(smaller letter) is placed before$X$(bigger letter). Hence, it will be subtracted.
$ \Rightarrow IX = 10 - 1 = 9$
Now, let’s solve the given expression.
$ \Rightarrow IX + XV + XX$
First, for the purpose of simplification, write the roman numbers in our regular numbers using the above two rules.
$ \Rightarrow 9 + 15 + 20$
Adding,
$ \Rightarrow 44$

$\therefore $ Our answer is option (C).

Note: Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers.
Some roman numerals in normal form
$I$ = $1$ $II$ = $2$ $III$ = $3$
$IV$ = $4$ $V$ = $5$ $X$ = $10$ $XX$ = $20$