The ratio of two numbers is [tex]\dfrac{2}{3}[/tex]. The sum of the numbers is 105. The two numbers are 42 & 63.
Given:
Ratio of two numbers = 2: 3
Sum of both the numbers = 105
To express any two numbers as a fraction we need to draw a line then we will be placing the smallest number above the line
Then, we will place the largest number below the line.
Now, we divide given two numbers having their common factors until it has no possibility to repeat the division.
The last two left indivisible numbers will become the ratio of two numbers.
To find the numbers lets assume the two numbers be x & y,
According to the question, ratio is given as 2:3
Therefore,
[tex]\rm \dfrac{x}{y} = \dfrac{2}{3} \;\;\;\;\;\;...............(1)\\\ x + y = 105 \;\;\;................(2)[/tex]
We will be solve, (1) we will put the values in terms of x [tex]\rm y = 1.5x[/tex]
Now we will substitute the values of 1 into 2
[tex]\rm x + 1.5x = 105\\\\2.5x = 105\\\\x = 42\\y= 63[/tex]
Therefore, The two numbers are x= 42 & y=63.
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