Direction : Consider the following for the two (02) items that follow : The budget allocations represented in a pie diagram under five different heads A, B, C, D and E are respectively 40%, 18%, 9%, 25% and 8%. The total budget allocation is ₹300.4 lakhs.
How much less amount is allocated to A and C together as compared to B, D and E together?
₹6.008 lakhs
Understanding Budget Allocation from a Pie Chart
The problem provides budget allocations across five different heads, A, B, C, D, and E, represented as percentages in a pie chart. The total budget allocation is given as ₹300.4 lakhs. We need to find the difference in the amount allocated to heads A and C combined, compared to the amount allocated to heads B, D, and E combined.
The given percentages for each head are:
- Head A: 40%
- Head B: 18%
- Head C: 9%
- Head D: 25%
- Head E: 8%
Let's first verify if the total percentage is 100%:
\(\text{Total Percentage} = 40\% + 18\% + 9\% + 25\% + 8\% = 100\%\)
This confirms the percentages represent the complete budget.
Calculating Combined Allocations
We need to find the total percentage allocated to (A + C) and the total percentage allocated to (B + D + E).
Percentage for (A + C) = Percentage of A + Percentage of C
Percentage for (A + C) = \(40\% + 9\% = 49\%\)
Percentage for (B + D + E) = Percentage of B + Percentage of D + Percentage of E
Percentage for (B + D + E) = \(18\% + 25\% + 8\% = 51\%\)
Note that \(49\% + 51\% = 100\%\), which accounts for the entire budget.
Converting Percentages to Amounts
The total budget allocation is ₹300.4 lakhs. To find the amount allocated to each group, we convert the percentages to fractions of the total budget.
Amount allocated to (A + C) = \(49\%\) of ₹300.4 lakhs
Amount allocated to (A + C) = \(\frac{49}{100} \times 300.4\) lakhs
Amount allocated to (A + C) = \(0.49 \times 300.4\) lakhs
Amount allocated to (A + C) = ₹147.196 lakhs
Amount allocated to (B + D + E) = \(51\%\) of ₹300.4 lakhs
Amount allocated to (B + D + E) = \(\frac{51}{100} \times 300.4\) lakhs
Amount allocated to (B + D + E) = \(0.51 \times 300.4\) lakhs
Amount allocated to (B + D + E) = ₹153.204 lakhs
Finding the Difference in Allocation
The question asks how much less amount is allocated to A and C together as compared to B, D and E together. This means we need to find the difference: (Amount B + D + E) - (Amount A + C).
Difference = Amount allocated to (B + D + E) - Amount allocated to (A + C)
Difference = ₹153.204 lakhs - ₹147.196 lakhs
Difference = ₹6.008 lakhs
Alternatively, we could calculate the difference in percentages first and then find that percentage of the total budget.
Difference in percentage = Percentage for (B + D + E) - Percentage for (A + C)
Difference in percentage = \(51\% - 49\% = 2\%\)
Difference in amount = \(2\%\) of ₹300.4 lakhs
Difference in amount = \(\frac{2}{100} \times 300.4\) lakhs
Difference in amount = \(0.02 \times 300.4\) lakhs
Difference in amount = ₹6.008 lakhs
Both methods yield the same result.
Summary of Calculations
| Group | Heads Included | Combined Percentage | Amount (₹ lakhs) |
|---|---|---|---|
| Group 1 | A, C | 49% | 147.196 |
| Group 2 | B, D, E | 51% | 153.204 |
| Difference | Group 2 - Group 1 | 51% - 49% = 2% | 153.204 - 147.196 = 6.008 |
The amount allocated to A and C together is ₹6.008 lakhs less than the amount allocated to B, D, and E together.
Revision Table: Key Budget Allocation Concepts
| Concept | Description | Calculation Example (using total budget ₹300.4 lakhs) |
|---|---|---|
| Percentage Allocation | The proportion of the total budget assigned to a specific head or group, expressed as a percentage. | Head A: 40% |
| Total Budget | The total amount of money available for allocation across all heads. | ₹300.4 lakhs |
| Amount Calculation | Converting a percentage allocation into a specific monetary value. | Amount for A = \(\frac{\text{Percentage of A}}{100} \times \text{Total Budget}\) |
| Difference Calculation | Finding the numerical difference between two allocated amounts. | Difference = Amount of Group 2 - Amount of Group 1 |
Additional Information on Pie Charts and Budgeting
Pie charts are commonly used graphical tools to represent parts of a whole. In budget allocation, a pie chart visually shows how the total budget is divided among different categories or heads. Each slice of the pie represents a budget head, and the size of the slice is proportional to the percentage of the total budget it receives.
- The sum of percentages of all slices in a pie chart is always 100%.
- To find the actual value of a slice (amount allocated to a head), you multiply the total budget by the percentage allocation (converted to a decimal or fraction).
- Budget allocation is the process of assigning available funds to different purposes, allowing organizations or individuals to plan and control spending.
- Understanding budget allocations is crucial for financial analysis and planning.
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