Question

Identify which symbol should appear in each sector in sections of a given pie chart.

Answer 1

Hint: In this question, first of all, find the total value of all the symbols by adding them. Now, find the percentage contribution of each symbol by using \[\dfrac{\text{Value of each symbol}}{\text{Total value}}\times 100\] and then match them with the given percentage in each sector of the pie chart.

Complete step-by-step solution:
In this question, we are given a pie chart and the value of each symbol and we have to find which symbol should appear in each sector. Let us solve this question.

Let us find the total value of all the symbols. From the figure, we get,
Total value of all symbols = (Value of Spade) + (Value of Diamond) + (Value of Cross) + (Value of Star)
So, we get,
\[\Rightarrow \text{Total value of all symbols}=800+700+550+450\]
\[\Rightarrow \text{Total value of all symbols}=2500\]
Now, let us find the percentage contribution of each symbol. We know that the percentage contribution of each symbol is \[\dfrac{\text{Value of each symbol}}{\text{Total value}}\times 100........\left( i \right)\]
By using equation (i), we get,
\[\text{Percentage contribution of Spade}=\dfrac{\text{Value of spade}}{\text{Total value of all symbols}}\times 100\]
\[\Rightarrow \text{Percentage contribution of Spade}=\left( \dfrac{800}{2500}\times 100 \right)\text{ Percent}\]
\[\Rightarrow \text{Percentage contribution of Spade}=32\text{ Percent}\]
\[\text{Percentage contribution of Diamond}=\dfrac{\text{Value of Diamond}}{\text{Total value of all symbols}}\times 100\]
\[\Rightarrow \text{Percentage contribution of Diamond}=\left( \dfrac{700}{2500}\times 100 \right)\text{ Percent}\]
\[\Rightarrow \text{Percentage contribution of Diamond}=28\text{ Percent}\]
\[\text{Percentage contribution of Cross}=\dfrac{\text{Value of cross}}{\text{Total value of all symbols}}\times 100\]
\[\Rightarrow \text{Percentage contribution of Cross}=\left( \dfrac{550}{2500}\times 100 \right)\text{ Percent}\]
\[\Rightarrow \text{Percentage contribution of Cross}=22\text{ Percent}\]
\[\text{Percentage contribution of Star}=\dfrac{\text{Value of star}}{\text{Total value of all symbols}}\times 100\]
\[\Rightarrow \text{Percentage contribution of Star}=\left( \dfrac{450}{2500}\times 100 \right)\text{ Percent}\]
\[\Rightarrow \text{Percentage contribution of Spade}=18\text{ Percent}\]
So, finally, we get the percentage contribution of each symbol as follows.
Spade – 32 %
Diamond – 28 %
Cross – 22 %
Star – 18 %
By matching the percentage contributions of the above symbols to that of the percentages in each sector of the given pie chart, we can place the symbols as follows.

Note: In this type of question, without actually calculating the contributions of each symbol, we can directly place the symbols in the pie – chart by using our approximation. As we can see that the highest percentage is given as 32 % and the highest value of the symbol is 800. So, 32 % will match with Spade. Similarly, the second-highest percentage given is 28 % and the second-highest value of the symbol is 700. So, 28 % will match with Diamond and so on. We can do it for all others as well. This approximation is good for objective type exams.