# Two numbers are in a ratio of \[5:3\]. Their sum is equal to \[80\], then find the larger number.

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**Hint:**In this question we are going to find the largest number by finding two numbers where its ratio and sum is given. The ratio of two quantities \[a\] and \[b\] in the same units, is the fraction \[\dfrac{a}{b}\] and we write it as \[a:b\]. The sign used to denote a ratio is ‘: (colon)’. Let us form equations from the given and solve it to find the numbers.

**Complete step-by-step solution:**

In order to determine the largest number from the two numbers.

Given two numbers are in the ratio of \[5:3\]

Now, let the numbers be \[5x\] and \[3x\]

We can form an equation with the two number and also given their sum is \[80\], that is,

\[5x + 3x = 80\].

Adding the x terms, then

\[8x = 80\]

\[ \Rightarrow x = \dfrac{{80}}{8}\]

on further simplification, then

\[ \Rightarrow x = 10\]

By substituting \[x\] value in the numbers be \[5x\] and \[3x\] .

The numbers, \[5x = 5(10) = 50\] and \[3x = 3(10) = 30\].

Hence, the two numbers are \[50\] and \[30\].

In our question we are asked to find the larger number, here \[50\] is greater than \[30\].

Therefore, the larger number is \[50\].

**Note:**Points to be remember when we are working on ratios:

1) The comparison or simplified form of two quantities of the same kind is known as ratio.

2) The ratio should exist between the quantities of the same kind.

3) While comparing two things, the units should be similar.

4) There should be significant order of terms.

5) Keyword to identify the ratio in a question is “to every”.

6) The comparison of two ratios can be performed, if the ratios are equivalent like the fractions.

7) In the ratio \[a:b\], we call \[a\] as the first term or antecedent and \[b\] the second term or consequent.

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