Question

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

Answer 1

Hint: Start by assuming one of the variable to be x and the other to be y, next step is to form equation on the basis of the question, and then solve those equations by making one of the variables equal by performing arithmetic operation so that we can cancel out that term, we get the value of one of the variables, we will put this value of variable in one of the equations to get the value of another variable.

Complete step by step answer:
Let two numbers be x and y.
Since,
$x + y = 240$ ….. (1)
$\dfrac{x}{y} = \dfrac{3}{5}$ ….. (2)
From (1) $y = 240 - x$.
Now let us substitute the obtained ‘y’ value in equation (2), we get
$
   \Rightarrow \dfrac{x}{{240 - x}} = \dfrac{3}{5} \\
   \Rightarrow 5x = 3(240 - x) \\
   \Rightarrow 5x = 720 - 3x \\
   \Rightarrow 5x + 3x = 720 \\
   \Rightarrow 8x = 720 \\
   \Rightarrow x = \dfrac{{720}}{{80}} = 90 \\
 $
Now, let us substitute the obtained value of x in ‘y’ we get
$ \Rightarrow y = 240 - 90 = 150$.

Hence the value of x is 90 and y is 150.

Note: There is another method to solve this question. Instead of taking two different variables x and y, we can only take 3x and 5x and take the sum of them to be equal to 240 as given in the question, and simplify to get the value of x and then find the value of 3x and 5x using the value of x obtained.