Question

A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey. From this pie chart answer the following:
(i) If 20 people liked classical music, how many young people were surveyed?
(ii) Which type of music is liked by the maximum number of people?
(iii) If a cassette company were to make 1000 CDs, how many of each type would they make?

Answer 1

Hint: Here, we will assume the total number of people surveyed by some variable and then multiply the percentage by the variable and then make it equal to 20 and then we will multiply the percentages by 1000 to find the required values.

Complete step by step solution:
(i) Let us assume that the total number of people surveyed is \[x\].

We know from the given pie chart the number of people who like classical is \[10\% \] of the total number of people.

Multiplying the \[10\% \] with \[x\], we get
\[
   \Rightarrow 10\% \times x \\
   \Rightarrow \dfrac{{10}}{{100}} \times x \\
   \Rightarrow \dfrac{1}{{10}} \times x \\
 \]

Since we are given that the number of people who liked classical music is 20, taking the above equation equal to 20, we get
\[ \Rightarrow \dfrac{1}{{10}} \times x = 20\]

Multiplying the above equation by 10 on both sides, we get
\[
   \Rightarrow \dfrac{1}{{10}} \times x \times 10 = 20 \times 10 \\
   \Rightarrow x = 200 \\
 \]

Thus, the total number of people were surveyed is 200.

(ii) In the given pie chart, we know that the maximum percentage shown is \[40\% \].

Therefore, the maximum number of people like light music.

(iii) First, we will find the total CD’s to be made by light music by multiplying the percentage by 1000, we get
\[
   \Rightarrow 40\% \times 1000 \\
   \Rightarrow \dfrac{{40}}{{100}} \times 1000 \\
   \Rightarrow 400 \\
 \]

 We will now find the total CD’s to be made by folk music by multiplying the percentage by 1000, we get
\[
   \Rightarrow 30\% \times 1000 \\
   \Rightarrow \dfrac{{30}}{{100}} \times 1000 \\
   \Rightarrow 300 \\
 \]

 We will find the total CD’s to be made by classical music by multiplying the percentage by 1000, we get
\[
   \Rightarrow 10\% \times 1000 \\
   \Rightarrow \dfrac{{10}}{{100}} \times 1000 \\
   \Rightarrow 100 \\
 \]

Now we will find the total CD’s to be made by light music by multiplying the percentage by 1000, we get
\[
   \Rightarrow 20\% \times 1000 \\
   \Rightarrow \dfrac{{20}}{{100}} \times 1000 \\
   \Rightarrow 200 \\
 \]

Therefore, the cassette company should make 400 CD’s of light music, 300 CD’s of folk music, 100 CD’s of classical music and 200 CDs of semi-classical music.


Note: In solving these types of questions, you should be familiar with the conversion of the percentage to fractions. to convert percentage into a fraction we need to divide the percentage by 100. Then use the given conditions and values given in the question after examining the pie chart carefully, to find the values. Some students take the percentages as their final answer, which is wrong.