Question

A cricket stadium manager counted the number of matches held in each month.

Months	Number of Matches
August	XCIV
September	LXXXVI
October	XCIX
November	CVI

In which month, the stadium had the lowest number of matches?
(a) August
(b) September
(c) October
(d) November

Answer 1

Hint: To solve the given question, we will first find out in which numeric system, the number of matches is written. Then we will convert this form into numerical form by using the conversions given I = 1, V = 5, X = 10, L = 50, C = 100. After converting the number of matches into numerical form, we will decide in which month the least number of matches are held and then accordingly we will select the correct option.

Complete step-by-step answer:
Before we start to solve the question, we must know in which numeric system the number of matches is written. These numbers are written in Roman Numeric System. In this numeric system, the numbers are represented by the combination of letters from the Latin alphabets. For converting Roman Numeric form to Numeric form, we will use the following conversions: I = 1, V = 5, X = 10, L = 50, C = 100.
Now, the number of matches played in August is XCIV. We know that X = 10 and C = 100 and as C is present after X, the value of XC will be (100 – 10) = 90. Similarly, the value of IV = (5 – 1) = 4. Thus, the number of matches played in August is 90 + 4 = 94.
Now, the number of matches played in September is LXXXVI. We know that L = 50, X = 10, V = 5 and I = 1. Thus, the number of matches played in September will be
\[\text{Number of Matches played in September}=50+3\left( 10 \right)+5+1\]
\[\Rightarrow \text{Number of Matches played in September}=50+30+5+1\]
\[\Rightarrow \text{Number of Matches played in September}=86\]
Now, the number of matches played in October is XCIX. We know that XC = 90 and IX = 9. Thus, the number of matches played in October = 90 + 9 = 99.
Now, the number of matches played in November is CVI. We know that C = 100, V = 5 and I = 1. Thus, the number of matches played in November is
\[\text{Number of Matches played in November}=100+5+1=106\]
Thus, we can say that the least number of matches are played in September.
Hence, option (b) is the right answer.

Note: We cannot write XCIV as 10 + 100 + 1 + 5 = 116. This is because X is ahead of C and 1 is ahead of V. When the smaller number is ahead of a larger number, then we find out the difference between them instead of adding them.