Question

Perform the following operations and write the answer in Roman form \[\]
$17+\left( 8-5 \right)5$\[\]
A. $\text{XI}$\[\]
B. $\text{XXXII}$\[\]
C. $\text{XV}$\[\]
D. $\text{XXV}$\[\]

Answer 1

Hint: We solve the given numerical expression $17+\left( 8-5 \right)5$ following BODMAS rule of arithmetic operations and find the result. We convert each of the Roman numerals present in the option to its decimal equivalent to check whether it is equal to result.

Complete step-by-step answer:
We know from the BODMAS rule that when we are given a numerical expression with multiple arithmetic operations and then we have first simplify the terms with brackets and then order ( or power or exponent) , Division, Multiplication, Addition, Subtraction in sequence.
The numerical expression that is given to us in the question is
\[17+\left( 8-5 \right)5\]
We see in the above expression that there four number and three arithmetic operations: addition, subtraction and multiplication with one bracket is given. We follow the BODMAS rule and solve the bracket first. We have
\[17+\left( 8-5 \right)5=17+3\times 5\]
We follow the BODMAS rule and operate multiply,
\[17+\left( 8-5 \right)5=17+3\times 5=17+15\]
We add the remaining terms and have,
\[17+\left( 8-5 \right)5=17+3\times 5=17+15=32\].
So the obtained value in the decimal number system is 32.
We know that roman numerals have symbols I, V, X, L etc. The decimal equivalents of the roman numerals are
\[I=1,V=5,X=10,L=50\]
Whenever a number is represented in roman numerals with more than one symbol say $A$ and $B$ where $A,B$ roman numerals are. Let us denote the decimal equivalent of $A$ be $d\left( A \right)$ and the decimal equivalent of $B$ be $d\left( B \right)$ and. Then the decimal equivalent of $AB$ be $d\left( AB \right)$. We have
\[\begin{align}
  & d\left( AB \right)=d\left( A \right)+d\left( B \right),\text{if }d\left( A \right)\ge d\left( B \right) \\
 & d\left( AB \right)=d\left( B \right)-d\left( A \right),\text{if }d\left( A \right) < d\left( B \right) \\
\end{align}\]
We can extend it for more than two symbols. Let us check the first option
A. Here the Roman numeral is XI where the decimal equivalent of X is $d\left( X \right)=10$ and the decimal equivalent of I is$d\left( I \right)=1$.Here we have $d\left( X \right)>d\left( I \right)$ we have the decimal equivalent of XI as
\[d\left( XI \right)=d\left( X \right)+d\left( I \right)=10+1=11\]
So we have $d\left( XI \right)\ne 32$ and option A is not correct. Let us check the first option B.
B. Here the Roman numeral is XXXII. We see that the decimal equivalent of all symbols after the first symbol X is then the decimal equivalent of first symbol X. So we have
\[\begin{align}
  & d\left( XXXII \right)=d\left( X \right)+d\left( X \right)+d\left( X \right)+d\left( I \right)+d\left( I \right) \\
 & \Rightarrow d\left( XXXII \right)=10+10+10+1+1=32 \\
\end{align}\]
So option B is correct and as numbers are uniquely represented in Roman numeral we do not need to check option C and D.\[\]

So, the correct answer is “Option B”.

Note: The decimal number 100 is represented in roman numerals by the symbol C, 500 by the symbol D, 1000 by the symbol M. The number 0 does not exist in roman numerals and no symbol can be repeated continuously more than 3 times. We can alternatively convert using the algorithm for decimal conversion.