Question

A shop has the following number of shoe pairs of different sizes
${\text{Size 2: 20, Size 3: 30, Size 4: 28, Size 5: 14, Size 6: 8}}$
Write this information in tabular form and find the percentage of each shoe size available in the shop.

Answer 1

Hint: Here we will first represent the data in a tabular format and then find the total number of shoes of all the sizes the shopkeeper has and then remove individual percentages for all the shoe sizes. Finally we get the required answer.

Formula used: ${\text{Percentage = }}\dfrac{{{\text{Part}}}}{{{\text{Whole}}}}{{ \times 100 \% }}$

Complete step-by-step solution:
The data given in the question can be represented in the tabular format as:

Size of shoes	Number of shoes
$2$	$20$
$3$	$30$
$4$	$28$
$5$	$14$
$6$	$8$
Total	$100$

From the above table made of the distribution we can conclude there is total $100$ shoes with the shopkeeper since:
$20 + 30 + 28 + 14 + 8 = 100$
Now we know there are $20$ shoes of size $2$ therefore, the total percentage of shoes of size $2$ is:
$\dfrac{{20}}{{100}} \times 100\% $
On simplifying we get:
$20\% $
Therefore $20\% $ shoes of the shopkeeper are of size $2$,
Now we know there is $30$ shoes of size $3$ therefore, the total percentage of shoes of size $3$ is:
$\dfrac{{30}}{{100}} \times 100\% $
On simplifying we get:
$30\% $
Therefore $30\% $ shoes of the shopkeeper are of size $3$,
Now we know there is $28$ shoes of size $4$ therefore, the total percentage of shoes of size $4$ is:
$\dfrac{{28}}{{100}} \times 100\% $
On simplifying we get:
$28\% $
Therefore $28\% $ shoes of the shopkeeper are of size $4$,
Now we know there is $14$ shoes of size $5$ therefore, the total percentage of shoes of size $5$ is:
$\dfrac{{14}}{{100}} \times 100\% $
On simplifying we get:
$14\% $
Therefore $14\% $ shoes of the shopkeeper are of size $5$,
Now we know there is $6$ shoes of size $6$ therefore, the total percentage of shoes of size $6$ is:
$\dfrac{6}{{100}} \times 100\% $
On simplifying we get:
$6\% $
Therefore $6\% $ shoes of the shopkeeper are of size $6$.
Therefore, the table could be rewritten along with the percentages as:

Size of shoes	Number of shoes	Percentage
$2$	$20$	$20\% $
$3$	$30$	$30\% $
$4$	$28$	$28\% $
$5$	$14$	$14\% $
$6$	$8$	$8\% $
Total	$100$	$100\% $

Note: Percentage stands for per century which means that it represents a fraction in terms of a century i.e. how much is its value when compared to $100$
While solving questions about percentages, it is good practice to try to keep the denominator a multiple of $100$ making it easier to simplify.
Percentages are used to simplify decimal point numbers to make it more readable and memorable. For example the number $0.42$ can be written as $42\% $.