Question

In a factory, the ratio of salary of skilled and unskilled workers is $5:3$ . Total salary for one day for both of them is Rs. $720$. Find the daily wages of skilled and unskilled workers.

Answer 1

Hint: Using the given ratio we get the salary of the skilled and unskilled workers to be $5x$ and $3x$ respectively. Adding these two and equating it to $720$ since it's given that the sum of their wages is $720$. Simplifying we get the value of $x$. And by substituting in $5x$ and $3x$ we get the salary of skilled and unskilled workers respectively.

Complete step-by-step solution:
We are given the ratio of the salary of skilled and unskilled workers to be $5:3$
Let $x$ be a positive integer, then the salary of a skilled worker is $5x$ and the salary of an unskilled worker is $3x$ .
We are given that the total salary of both skilled and unskilled workers for one day is Rs. $720$.
Hence, we get
$5x + 3x = 720$
Adding the like terms we get,
$8x = 720$
Dividing by $8$ on both sides we get the value of $x$
$ \dfrac{{8x}}{8} = \dfrac{{720}}{8} $
$ \Rightarrow x = 90 $
We know that the salary of a skilled worker is $5x$.
Substituting the value of $x$ ,
Salary of skilled worker $ = 5\left( {90} \right) = 450$
We know that the salary of unskilled workers is $3x$.
Substituting the value of $x$ ,
Salary of unskilled worker $ = 3\left( {90} \right) = 270$
Therefore, the salary of skilled worker is Rs. $450$ and the salary of unskilled worker is Rs. $270$.

Note: Whenever we are dealing with problems related to ratio many students tend to take the salary of the skilled and unskilled workers to be $5$ and $3$. But it is a mistake they are $5x$ and $3x$ where $x$ is a positive integer. A ratio can be expressed in two ways either $a:b$ or $\dfrac{a}{b}$ .