Question

Two numbers are in the ratio \[5:3\]. If they differ by 18, what are the numbers?

Answer 1

Hint: We will first consider the given ratio that is \[5:3\]. We will next consider that \[x\] represents the common ratio therefore as the two numbers are in the ratio \[5:3\] implies that \[5x\] and \[3x\] are the two numbers. Now, the difference between two numbers is given as 18 so, we will form an equation and evaluate the value of \[x\] from that equation and then substitute the value of \[x\] in the two numbers \[5x\] and \[3x\] which will give us the required answer.

Complete step-by-step answer:
We will first consider the given ratio of two numbers as \[5:3\].
The objective is to find the two numbers.
Now, we will let that common ratio be shown by \[x\].
Hence, the two numbers are represented as \[5x\] and \[3x\] respectively.
As we know that the difference of the two numbers is given by 18.
So, we will form an equation using this. Thus, we get,
\[
   \Rightarrow 5x - 3x = 18 \\
   \Rightarrow 2x = 18 \\
 \]
Next, we will divide both the sides of the above equation by 2 to obtain the value of \[x\].
Hence, we get,
\[
   \Rightarrow \dfrac{{2x}}{2} = \dfrac{{18}}{2} \\
   \Rightarrow x = 9 \\
 \]
Now, we will find the values of the two numbers by substituting the value of \[x\] in \[5x\] and \[3x\].
Hence, the first number is \[5x = 5 \times 9 = 45\]
And the second number is \[3x = 3 \times 9 = 27\]
Thus, the two numbers are 45 and 27.

Note: Form the equation properly after reading the given statement carefully. As the ratio is given so we can write the numbers in the terms of \[x\] where \[x\] shows the common ratio. Simplify the equation properly without doing any calculation mistakes. While substituting the value of \[x\], do the calculation carefully.