Question

The following pie chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie chart and answer the questions based on it.

(i) If for a certain quantity of books, the publisher has to pay Rs. $30,600$ as printing cost, then what will be the amount of royalty to be paid for these books?
(ii) What is the central angle of the sector corresponding to the expenditure incurred on royalty?
(iii) By what amount is the promotion cost on the book less than the printing cost?

Answer 1

Hint: In this problem we need to study the given pie chart and answer the given questions. For this we will first assume the total expenditure as $p$ and from the chart we will write the amount to be paid for each expenditure. In the first question we have given the printing cost for a certain quantity of books. So we will equate the amount to be spent on printing cost to the given value and calculate the value of $p$ which is the total expenditure. For the $p$ value we can simply calculate the royalty to be paid. In the second question we need to find the central angle of the sector corresponding to the expenditure incurred on royalty. For this we will use the formula ${\displaystyle \frac{x}{100}}\times 360{}^{\circ }$ where $x$ is the percentage related to the royalty. In the third question we need to find by what amount the promotion cost on the book is less than the printing cost. For this we will calculate the difference between the promotion cost and the printing cost.

Complete step by step answer:
Given pie chart is

Let us assume the total expenditure is to be$p$.
From the above pie chart we can write
Transportation cost for the book is $10\mathrm{\%}p$ .
Promotion cost for the book is$10\mathrm{\%}p$.
Binding cost for the book is $30\mathrm{\%}p$ .
Paper cost for the book is $25\mathrm{\%}p$ .
Printing cost for the book is $20\mathrm{\%}p$ .
Royalty cost for the book is $15\mathrm{\%}p$ .
(i)
Given that the printing cost paid by the publisher is Rs. $30,600$.
But the printing cost for the total expenditure $p$ is $20\mathrm{\%}p$. Equating the both the values, then we will get
$20\mathrm{\%}p=30600$
Simplifying the above equation by using basic mathematical operations, then we will have
$\begin{array}{rl}& {\displaystyle \frac{20}{100}}\times p=30600\\ & \Rightarrow p=30600\times {\displaystyle \frac{100}{20}}\\ & \Rightarrow p=153000\end{array}$
Hence the total expenditure is given by $1,53,000$ .
The royalty cost to be paid by the publisher is given by $15\mathrm{\%}p$.
Now the royalty cost for the expenditure amount $1,53,000$ is given by
$\begin{array}{rl}& 15\mathrm{\%}p=15\mathrm{\%}\text{of }153000\\ & \Rightarrow 15\mathrm{\%}p={\displaystyle \frac{15}{100}}\times 153000\\ & \Rightarrow 15\mathrm{\%}p=22950\end{array}$
Hence the royalty cost for the book is Rs. $22,950$.
(ii)
We can observe the percentage of royalty cost for the book as $15\mathrm{\%}$.
Now the central angle made by the sector corresponding to the expenditure incurred on royalty is given by
$\begin{array}{rl}& {\displaystyle \frac{x}{100}}\times 360{}^{\circ }={\displaystyle \frac{15}{100}}\times 360\\ & \Rightarrow {\displaystyle \frac{x}{100}}\times 360{}^{\circ }=54{}^{\circ }\end{array}$
Hence the central angle made by the sector corresponding to the expenditure incurred on royalty is $54{}^{\circ }$ .
(iii)
We have the promotional cost as $10\mathrm{\%}p$ and printing cost as $20\mathrm{\%}p$.
The difference between two costs is given by
$20\mathrm{\%}\text{ of }p-10\mathrm{\%}\text{of }p=10\mathrm{\%}\text{of }p$
Hence the promotional cost is $10\mathrm{\%}$ less than the printing cost.
If we consider the total expenditure amount as Rs. $1,53,000$. Now the amount that promotional cost is less that printing cost is given by
$\begin{array}{rl}& 10\mathrm{\%}\text{ of }p={\displaystyle \frac{10}{100}}\times 153000\\ & \Rightarrow 10\mathrm{\%}\text{ of }p=15300\end{array}$
Hence the promotional cost is Rs. $15300$ less than printing cost.
Note: Reading pie charts is the main important step for this problem. In the pie chart we will have a certain aspect along with its percentage in total. So we have assumed the total expenditure and written each aspect individually according to their percentages.