 QUESTION

# Find the sum of the expression: IX + XV + XX = _________(a) 45(b) 35(c) 44(d) 40

Hint: Use the roman numerals knowledge to write IX as 9, XV as 15 and XX as 20. Then add these to find the desired result.

We have been asked to find the value of the given expression, that is, IX + XV + XX.
Actually the term whose sum we have been asked to find is called the Roman numerals.
Roman numerals is a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe. Numbers in this system are represented by a combination of letters from present in English alphabet. Modern usage employs seven symbols each with a fixed integer value, as shown in the following table:

 Symbol I V X L C D M Value 1 5 10 50 100 500 1000

If ‘I’ is placed on the left hand side, then the value of the symbol is subtracted by ‘1’. For example:
IV becomes 5 – 1 = 4
Similarly, if ‘I’ is placed on the right hand side, then the value of symbols is added by ‘1’. For example:
VI becomes 5 + 1 = 6
This same procedure is followed for all the symbols.
IX here ‘I’ is place on left of X, so we get
IX = 10 – 1 = 9………..(i)
Similarly, in XV, ‘V’ is placed on the right hand side of the ‘X’, so we add as shown below:
XV = 10 + 5 = 15……(ii)
Now, XX = 10 + 10 = 20………(iii)
So, the given expression is,
IX + XV + XX
Substituting the values from equation (i), (ii) and (iii), we get
IX + XV + XX = 9 + 15 + 20 = 44
Hence, the correct answer is option (c).

Note: Students should have knowledge about symbols, notations and other facts related to the roman numerals. They should also be careful about substituting the values otherwise the answer will be wrong.