Question

The fourth proportional to 5, 8, 15 is
A) 24
B) 18
C) 20
D) 21

Answer 1

Hint: We have been given three numbers, if the ratios of first and second will be proportional to that of third and fourth, then the fourth value will be known as their fourth proportional. Using this fact, we can find the required value of fourth proportional to the given numbers. The ratio in fraction can be given as:
$a:b={\displaystyle \frac{a}{b}}$
And the proportionality as $a:b=c:d$ where $d$ is the fourth proportional.

Complete step by step solution:
If four integers a, b, c, d are in proportion, they can be written as $a:b=c:d$
As proportion denotes equivalency between the two ratios. Here, $d$ is called the fourth proportional to $a,b$ and $c$.
In fraction, this proportionality can be written as:
$\Rightarrow {\displaystyle \frac{a}{b}}={\displaystyle \frac{c}{d}}$
For the given question, the four values are:
$a=5$
$b=8$
$c=15$
Let $d=x$
The fourth proportional that is required to be calculated is supposed to be $x$ here. Substituting the values, we get:
$\Rightarrow {\displaystyle \frac{5}{8}}={\displaystyle \frac{15}{x}}$
The value of x can be calculated by the cross multiplication of the obtained value.
$$\begin{gathered} \Rightarrow 5\times x=15\times 8 \\ \Rightarrow 5x=120 \\ \Rightarrow x={\displaystyle \frac{120}{5}} \\ \Rightarrow x=24 \end{gathered}$$
Therefore, the fourth proportional to 5, 8, 15 is 24.

Hence, the correct answer is “Option A”.

Note:
We can denote the proportionality of numbers with either ‘::’ sign or ‘=’ sign. The proportionality of integers can also be denoted as: $a:b::c:d$
This shows that the ratio of $a$ and $b$ is proportional to that of $c$ and $d$. The ratio is denoted by ‘:’ sign between the quantities. In this formula, $b$ and $c$ are called mean terms while $a$ and $d$ are known as extremes.