Introduction To Proportion

I. Introduction

When multiple ratios are equal, these ratios are said to be $\underline{in\ proportion}$.

Let us say, you are taking the photocopy of a rectangular image if size $20\ cm \times 30\ cm$. But you want a larger copy with the breadth as $25\ cm$, and you also do not not want the picture to get distorted, that is the ratio of the length and the breadth should remain the same.

So, the breadth changed from $20\ cm$ to $25\ cm$, how much should be the new length so that the ratio is same.

Let us say that the new length is $l$.

So we know that:

$\dfrac{20}{30} = \dfrac{25}{l}$

Here we can say that the ratio of the breadth is to length is same for the image and its copy. So the ratios are in proportion. The symbol $::$ is used to denote proportion.

We will write this as,

$20:30::25:l$

How do we find the value of $l$?

We know that $\dfrac{20}{30} = \dfrac{25}{l}$

$\texttip{\Rightarrow}{follows that} 20l = 30 \times 25$

$\texttip{\Rightarrow}{follows that} l = \dfrac{30 \times 25}{20}$

$\texttip{\Rightarrow}{follows that} l = \dfrac{3 \times 25}{2}$

$\texttip{\therefore}{therefore} l = 37\dfrac{1}{2}$

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Let us try the following question before we proceed further with this:

--------- Reference to question: 65729f24-f971-4aed-b004-11128f64a300 ---------

Introduction To Ratio