Question

Express the following as a ratio in the simplest form:
$2$ dozen to $1$ score.

Answer 1

Hint: The ratio of two quantities $x$ and $y$ is written in the form $x:y$ which is calculated by writing the quantities in fraction and then converting the fraction into simplest form. The given two quantities must be in the same units.

Complete step-by-step solution:
Given: we have to find a ratio of $2$ dozen to $1$ score.
We know that one dozen of any object is equal to $12$ objects. So
$2$ dozen $ = 2 \times 12 = 24$ objects.
We also know that $1$ score of any object is equal to $20$ objects.
Now, to find the ratio of $2$ dozen to $1$ score of any objects, the quantities are written in the form of fraction that is $\dfrac{{24}}{{20}}$.
Now, converting the above written fraction into the simplest form we get $\dfrac{{24}}{{20}} = \dfrac{6}{5}$.

Thus, the ratio of $2$ dozen to $1$ score is $6:5$.

Note: Similarly, the ratio of $1$ year and $2$ months to $x$(few) days is calculated. For this, first convert $1$ year and $2$ months into days and then write both the quantities in fraction and convert the fraction into the simplest form. Then we get the required ratio.
It is blunder to find the ratio of two quantities which are not the same measuring units. We can not write $2$ kilograms rice and $2$ litres oil in the form of ratio.
It is also important to know that the ratio is a dimensionless quantity because if we write two quantities having the same unit in fraction form then the unit is cancelled out and we get only numerals which is a dimensionless quantity.