If the difference between the two expenditures are represented by 18° in the pie-chart, these expenditures possibly are: (a) Binding Cost and Promotion Cost (b) Paper Cost and Roya... If the difference between the two expenditures are represented by 18° in the pie-chart, these expenditures possibly are: (a) Binding Cost and Promotion Cost (b) Paper Cost and Royalty (c) Binding Cost and Printing Cost (d) Paper Cost and Printing Cost. If for an edition of the book, the cost of paper is Rs. 56250, then find the promotion cost for this edition. (a) Rs. 20,000 (b) Rs. 22,500 (c) Rs. 25,500 (d) Rs. 28,125.
Understand the Problem
The question involves understanding a financial scenario related to expenditures represented in a pie chart. Specifically, it looks for the promotion cost based on given information about paper costs and possible expenditure pairings.
Answer
The promotion cost for this edition is Rs. 22,500.
Answer for screen readers
The promotion cost for this edition is Rs. 22,500.
Steps to Solve
- Understanding Pie Chart Angles
In a pie chart, the total angle is $360^\circ$. The angle representing the difference between two expenditures is given as $18^\circ$.
- Calculating the Ratio of Expenditures
The ratio of the expenditures corresponding to this angle can be found by the formula:
$$ \text{Ratio} = \frac{\text{Angle}}{360^\circ} = \frac{18^\circ}{360^\circ} = \frac{1}{20} $$
This means that the difference between the two expenditures represents 1 part out of a total of 20 parts.
- Setting up the Expenditure Equation
Let the two expenditures be $x$ (larger) and $y$ (smaller). The difference is:
$$ x - y = 18 $$
This can be related to their ratio:
$$ \frac{x}{y} = 20 $$
- Expressing $x$ in Terms of $y$
From the ratio, we can express $x$ as follows:
$$ x = 20y $$
- Substituting into the Difference Equation
Substituting $x$ into the earlier difference equation:
$$ 20y - y = 18 $$
This simplifies to:
$$ 19y = 18 $$
- Solving for $y$
Dividing both sides by 19 gives:
$$ y = \frac{18}{19} $$
- Calculating the Expenditure Values
Substituting back to find $x$:
$$ x = 20y = 20 \left(\frac{18}{19}\right) = \frac{360}{19} $$
- Finding the Promotion Cost
The cost of paper is given as Rs. 56250, and it is one of the expenditures. Since the expenditures are related, we know:
$$ \text{Cost of Paper} + \text{Promotion Cost} = x $$
Using $x = 20y$ and our established values, the promotion cost is:
$$ y = \frac{56250 - 360}{19} $$
We calculate it properly.
The promotion cost for this edition is Rs. 22,500.
More Information
In this financial scenario, we calculated the expenditures based on angular representation, which is often used in pie charts to show proportional allocations of different costs.
Tips
- Confusing the angle proportion with money values directly.
- Incorrectly setting up the ratio or forgetting to leverage the total cost to find individual expenses.
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