Question

In a football match the ratio of total number of players of both the teams to the number of referees is\[\]
A.10:2\[\]
B. 11:2\[\]
C. 22:2\[\]
D. 22:1 \[\]

Answer 1

Hint: We know that there are 11 players from each team who can play on the ground. So we first find the total number of players who can play on the ground. There is only 1 referee in the ground. We find the ratio of total players to the number of referees. \[\]

Complete step by step answer:
A ratio is a fraction with both numerator and denominator as positive integers expressed in standard form. The standard of a fraction is $\dfrac{p}{q}$ where both $p$ and $q$ are positive integers and the highest common factor of $p$ and $q$ is 1. It means $p$ and $q$ are co-prime or relative prime. \[\]
The ratio between two positive integers numbers $A$ and$B$ is written as $a:b$ and is given as
\[A:B=\dfrac{\dfrac{A}{n}}{\dfrac{B}{n}}=\dfrac{a}{b}=a:b\]
  Where $n$ is the greatest common divisor of $A$ and $B$.
If two numbers $A$ and $B$ are in a ratio $a:b$ and then for some positive integer $k$ if multiplied, $kA$ and $kB$ will so have the same ratio $a:b$.\[\]
If two numbers $A$ and$B$ are in a ratio $a:b$ and then for some positive integer $k$, if divided $\dfrac{A}{k}$ and $\dfrac{B}{k}$ will so have the same ratio$a:b$ where $k$ is a factor of both $A$ and $B$.\[\]
We are asked to find the ratio of the total number of players on the ground the number to referee. We know that in football there are 11 players in each team who can play on the ground. So there total $11+11=22$ players on the ground. Even the team manager replaces a player the total number of players will remain the same. There is also 1 referee to enforce the law of the game. So the ratio of the total number of players to the number of referees is 22:1. So the correct option is D.\[\]

Note:
 We need to be careful that questions ask the total number of players on the ground not in the stadium which has extra 5 substitute players from both sides. So total $22+5+5=32$ players and the ratio 32:1. In cricket there are two umpires, so the ratio will be $22:2=11:1$.