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Difficulty: HardTables and Data Grids

The table below presents the operational metrics for Agricultural Processing Units across four districts of a state for FY 2025–26:

DistrictTotal Processing Capacity (in '000 MT)Operational Units CountTotal Raw Produce Received (in '000 MT)Processing Efficiency Rate (%)
District A4501836085%85\%
District B6002448090%90\%
District C5002042080%80\%
District D3501432075%75\%

*Note: Processing Efficiency Rate is defined as the percentage of Total Raw Produce Received that is converted into finished products. The remaining portion of received raw produce is lost as processing waste.*

What is the overall average processing waste (in '000 Metric Tonnes) per operational unit across all four districts combined?

Answer: 3.5 '000 MT per unit

Answer

The overall average processing waste per operational unit across all four districts combined is 3.53.5 thousand Metric Tonnes.
The correct answer is derived by first finding the waste volume for each district based on raw produce received: District A (360×0.15=54360 \times 0.15 = 54), District B (480×0.10=48480 \times 0.10 = 48), District C (420×0.20=84420 \times 0.20 = 84), and District D (320×0.25=80320 \times 0.25 = 80). Summing these gives a combined total waste of 266266 thousand MT. Dividing this total waste by the total count of operational units (18+24+20+14=7618 + 24 + 20 + 14 = 76) yields 26676=3.5\frac{266}{76} = 3.5 thousand MT per unit.

Step-by-Step Solution

1
Calculate the processing waste percentage for each district
District A waste rate = 100%−85%=15%100\% - 85\% = 15\%; District B waste rate = 100%−90%=10%100\% - 90\% = 10\%; District C waste rate = 100%−80%=20%100\% - 80\% = 20\%; District D waste rate = 100%−75%=25%100\% - 75\% = 25\%.
Processing waste is the complement of processing efficiency rate.
2
Calculate total processing waste generated in each district in '000 MT
District A waste = 360×0.15=54360 \times 0.15 = 54 '000 MT; District B waste = 480×0.10=48480 \times 0.10 = 48 '000 MT; District C waste = 420×0.20=84420 \times 0.20 = 84 '000 MT; District D waste = 320×0.25=80320 \times 0.25 = 80 '000 MT.
Absolute waste is obtained by multiplying Total Raw Produce Received by the waste rate.
3
Calculate total waste and total operational units across all four districts combined
Total Waste = 54+48+84+80=26654 + 48 + 84 + 80 = 266 '000 MT. Total Operational Units = 18+24+20+14=7618 + 24 + 20 + 14 = 76 units.
Aggregating metrics across districts is required to find the combined weighted average.
4
Divide total combined waste by total combined operational units
Average Waste per Unit = 26676=3.5\frac{266}{76} = 3.5 '000 MT per unit.
Overall average metric equals total aggregate waste divided by total aggregate count of units.

Key Concept

Weighted Average and Percentage Calculation from Data Grids
Estimated Time:2m 30s
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Topics

Tables and Data Grids

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