Question

Divide $30$ in the ratio of $3:2$ ?

Answer 1

For dividing a number in a fixed ratio one have to assume a variable in order to make a algebraic equation and solve it, this assumed variable is only for deriving the equation and there is no any case and property for selection of the variable.

Complete step by step solution:
Assuming a variable$x$, for deriving an equation in order to get the result. Here, the given ratio should be multiplied with the variable and then write in the summation form and then equating it to the given number, we get:

$$3x + 2x = 30 \\\ 5x = 30 \\\ x = \dfrac{{30}}{5} \\\ x = 6 \\\$$

Now here we obtain the value of the assumed variable now to obtain the number we have to just
multiply the variable value with the given ratio, we get:

$$3x = 3 \times (6) = 18 \\\ 2x = 2 \times (6) = 12 \\\$$

So our required number is $18,\,12$

Additional Information: Solving for ratio only needs the formation of the equation according to the given context in question, once the equation is obtained then it’s just a simple algebraic equation and you have to deal with it.

Note: Any ratio given means it explains the difference between the next numbers we are going to obtain after solving the equation, or you can understand as ratio defines the breaking of a complete number into two or three parts such that when adding all the numbers obtained the initial given number.