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Question

Difficulty: MediumRatios, Rates, and Percentages

A commercial bakery operates three distinct production units—Unit X, Unit Y, and Unit Z—to fulfill daily shipments of bread loaves:

- Unit X produces 150150 loaves per hour, with 4%4\% discarded due to minor defects.
- Unit Y produces 200200 loaves per hour, with 5%5\% discarded due to minor defects.
- Unit Z produces 250250 loaves per hour, with 2%2\% discarded due to minor defects.

Match each production unit on the left with its corresponding net yield of non-defective loaves produced during an 88-hour shift on the right.

  • Unit X1,152 non-defective loaves
  • Unit Y1,520 non-defective loaves
  • Unit Z1,960 non-defective loaves

Answer

Unit X matches with 1,152 non-defective loaves; Unit Y matches with 1,520 non-defective loaves; Unit Z matches with 1,960 non-defective loaves.
Each unit's net non-defective yield is derived by calculating gross output over 8 hours (Hourly Rate × 8) and multiplying by (1−Defect Rate)(1 - \text{Defect Rate}). Unit X yields 1,200×0.96=1,1521,200 \times 0.96 = 1,152, Unit Y yields 1,600×0.95=1,5201,600 \times 0.95 = 1,520, and Unit Z yields 2,000×0.98=1,9602,000 \times 0.98 = 1,960.

Step-by-Step Solution

1
Calculate total gross production for each unit over an 8-hour shift.
Unit X produces 150×8=1,200150 \times 8 = 1,200 loaves; Unit Y produces 200×8=1,600200 \times 8 = 1,600 loaves; Unit Z produces 250×8=2,000250 \times 8 = 2,000 loaves.
Gross production equals hourly rate multiplied by duration.
2
Calculate the non-defective percentage for each unit.
Unit X non-defective rate is 100%−4%=96%100\% - 4\% = 96\%; Unit Y non-defective rate is 100%−5%=95%100\% - 5\% = 95\%; Unit Z non-defective rate is 100%−2%=98%100\% - 2\% = 98\%.
The non-defective rate is the complement of the discard percentage.
3
Multiply gross output by the non-defective rate to determine net yield.
Unit X yield is 1,200×0.96=1,1521,200 \times 0.96 = 1,152; Unit Y yield is 1,600×0.95=1,5201,600 \times 0.95 = 1,520; Unit Z yield is 2,000×0.98=1,9602,000 \times 0.98 = 1,960.
Applying the non-defective fraction gives the final usable loaf count for each unit.

Key Concept

Work rate and net yield calculation using percentages
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Topics

Ratios, Rates, and Percentages

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