Question

For a survey, a company decided to call $7$ out of every $5000$ people. How many people should be called in a town of $78,000$ people?

Answer 1

Hint: For this type of question, we use the unitary method to solve. Here we must analyze that out of $5000\;$ people, $7\;$ people are selected; Then out of $78,000\;$ people how many of them will be selected? So here we perform cross-multiplication as used in the unitary method and then we evaluate the expression to get the answer.

Complete step by step solution:
Given that, a company decided to call $7\;$ out of every $5000\;$ people.
We must find how many people the company will call out of a group of $78000\;$ people.
Here we shall put it more understandably.
Out of $5000\;$ people, $7\;$ people are selected.
Then out of $78,000\;$ people how many of them will be selected?
Which can be written in unitary method form as,
$5000\;$ people -- $7$ selected.
$78000\;$ people -- $?\;$ selected.
Here we perform cross multiplication to find out how many people are selected.
On Cross multiplying we get,
$\Rightarrow \dfrac{78000\times 7}{5000}$
On further simplifying we get,
$\Rightarrow \dfrac{78\times 7}{5}$
$\Rightarrow \dfrac{546}{5}$
On further evaluating we get,
$\Rightarrow 109.2$
Since here our units are people, people cannot be expressed in decimal values.
Hence, we round off the value to $109\;$ .

Therefore, out of $5000\;$ people, $7\;$ people are selected; Then out of $78,000\;$ people $109\;$ of them will be selected.

Note: The Unitary method which we are using to solve is a technique for solving a problem by first finding the value of a single quantity, and then finding the necessary value by cross-multiplying the single quantity value. In our question the value of a single quantity which will be $5000\;$ people as $7\;$
is given and we must find the necessary value for $78000\;$ quantity.