Question

How do you solve this? The ratio of two integers is $13:6$. The smaller integer is $54$. Find the larger integer.

Answer 1

Hint: In this question we have been given with a ratio of two numbers in the most simplified manner. We have also been given the smaller integer as $54$. Since we do not know the greater integer, we will consider it to be $x$ and equate it with the given ratio and use cross multiplication and simplify, to get the value of $x$ which is the required solution.

Complete step by step solution:
We know that the ratio of two integers is $13:6$ and the smaller integer has the value $54$. Now in the ratio $13:6$, we can see that $6$ is the smaller ratio. This implies that $54$ will be equated to $6$.
And since we have the other value unknown, we will equate $x$ with $13$.
Mathematically we can write it as:
$\Rightarrow \dfrac{x}{54}=\dfrac{13}{6}$
On transferring the term $54$ from the left-hand side to the right-hand side, we get:
$\Rightarrow x=\dfrac{13\times 54}{6}$
On multiplying the terms in the numerator, we get:
$\Rightarrow x=\dfrac{702}{6}$
On simplifying, we get:
$\Rightarrow x=117$

Therefore, the greater integer is $117$ which is the required solution.

Note: Ratio is based on the concept of fractions, a ratio is basically a fraction in the form of $\dfrac{a}{b}$ represented as $a:b$. It is used to represent a value in terms of another value.
Proportion is a concept in ratio and it represents when two ratios are the same.
A ratio of two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ can be represented as $a:b::c:d$
A ratio has to be with similar quantities for comparison, while comparison of two quantities the units of both the quantities should be the same.