Question

The sum of natural numbers is 240 and they are in the ration, 3:5. Find the numbers.

Answer 1

Hint: Here is the question the ratio of two numbers given so common factor is cancelled as we know that ratio is always in the simplest form. Let us assume that the common number is \[x\] so numbers will be $3x\text{ }\And \text{ 5}x$.

Formula used:
Sum of two natural number is 240
i.e. $\text{First number}+\text{Second number}=\text{Total}$
Complete step-by-step answer:
In this type question we will assume an imaginary number\[x\], so the numbers becomes\[~3x\text{ }and\text{ }5x.\]
Let the one number is \[3x\] Other number is 5x
The according to question
3x+5x=240
$\Rightarrow$ 8x=240
$\Rightarrow$ x=$\dfrac{240}{8}$
$\Rightarrow$ x=30
So the numbers are 90, 150 \[(As\text{ }3\times 30,\text{ 5}\times \text{30})\]

Additional Information:
 Students can approach the question by this approach like$\begin{align}
  & \text{First number}=x \\
 & \text{Second number}=240-x \\
\end{align}$
 According to question
$\begin{align}
  & \dfrac{x}{240-x}=\dfrac{3}{5} \\
 &\Rightarrow 5x=3\left( 240-x \right) \\
 &\Rightarrow 5x=720-3x \\
 &\Rightarrow 5x+3x=720 \\
\end{align}$
$\begin{align}
  & \Rightarrow 8x=720 \\
 & \Rightarrow x=\dfrac{720}{8}=90 \\
\end{align}$
 $\begin{align}
  &\Rightarrow \text{First number}=90 \\
 &\Rightarrow \text{Second number}=240-90 \\
 &\Rightarrow \text{ }130 \\
\end{align}$

Note: In first approach we solved the question by multiplying by the common factor & in Second approach we assume first number \[x\] & other $240-x$ then we equate by their ratio.