Question

If 6 interns and 2 managers working together can do five times the work that an intern and a manager can do. Calculate the ratio of the working capacities of an intern and a manager?​

Answer 1

Hint: Here in this question, we have to find the ratio of the working capacities of an intern and a manager. For this, let’s take the work done by an intern as $$x$$ and work done by manager as $$y$$ then by using the given condition in question and simplify by using a basic arithmetic operation to get the required solution.

Complete step by step solution:
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division. Or The division or fraction of the first quantity and second quantity is called ratio.
If the ratio of a and b can be expressed as $$a:b$$ or $$\dfrac{a}{b}$$.
Consider the given question:
Given,
Number of interns = 6
Number of Managers = 2
Let’s take the work done by an interns$$ = x$$
Let’s take the work done by manager $$ = y$$
Therefore, according to the question – “6 interns and 2 managers working together can do five times the work that an intern and a manager can do”.
$$ \Rightarrow \,\,6x + 2y = 5\left( {x + y} \right)$$
$$ \Rightarrow \,\,6x + 2y = 5x + 5y$$
Subtract 5x and 2y on both sides, then we have
$$ \Rightarrow \,\,6x - 5x = 5y - 2y$$
On simplification, we get
$$ \Rightarrow \,\,1x = 3y$$
or
$$\therefore \,\,\,\,\,\,\dfrac{x}{y} = \dfrac{1}{3}$$
Therefore, the ratio of the working capacities of an intern and a manager is $$1:3$$.
So, the correct answer is “$$1:3$$”.

Note: Ratio problems are word problems that use ratios to relate or compare the different items in the question. Remember The main things to be aware of for ratio problems are to change the quantities to the same unit if necessary and it can be simplified or solved by the proper arithmetic operations.