Question

# Write the ratio of second quantity to first quantity in the reduced form: 5 dozen pens, 120 pens

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Hint:To reduce the ratio, first convert the ratio in fraction form.Proceed to reduce the fraction by dividing the numerator and denominator by their HCF.Finally, convert the fraction into ratio.A ratio compares values. A ratio says how much of one thing there is compared to another thing.

Given that
First quantity as 5 dozen pens and
second quantity as 120 pens
For writing the ratio of the given quantities,
First, we have to keep both quantities in the same unit.
Therefore, first quantity can be written as 60 pens because 1 dozen = 12 quantity
Now, as per the question,
Ratio of second quantity to first quantity can be written as
120 pens: 60 pens
$\Rightarrow$120: 60
$\Rightarrow \dfrac{{120}}{{60}}$
Since, HCF of 60 and 120 is 60.
Thus, on dividing the numerator and denominator, we have
$\begin{gathered} \Rightarrow \dfrac{{120 \div 60}}{{60:60}} \\ \Rightarrow \dfrac{2}{1} \\ \Rightarrow 2:1 \\ \end{gathered}$

$\therefore$Required ratio = 2:1

Note:The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.Ratios are the comparison of two quantities or more quantities (having the same units) that we express as a fraction. The concept of equivalent fractions allows the ratios of different physical quantities to be the same sometimes. Thus, a ratio is a general term independent of a unit and we use it across multiple platforms.First term of the ratio is known as antecedent and the second term is known as consequent.