A batch of 1000 kg of apples containing 6.2% bruised apples is sorted by an electronic colour sorter. The sorted apples contain 927.3 kg red apples and 17.4 kg bruised apples. Remaining red and bruised apples are delivered at the rejection outlet of the sorter. Overall effectiveness of the sorter is __________.
Official Answer Key:
0.70 to 0.72
Step-by-Step Solution & Explanation
• Feed: bruised = 6.2% of 1000 = 62 kg; sound (“red”) = 1000–62 = 938 kg.
• Accepted stream: sound apples correctly accepted = 927.3 kg; bruised apples wrongly accepted = 17.4 kg. Bruised correctly rejected = 62–17.4 = 44.6 kg.
• Overall effectiveness of a two-component separator = (fraction of desired component correctly recovered) × (fraction of undesired component correctly rejected).
• Recovery of sound apples = 927.3/938 = 0.9885. Rejection of bruised apples = 44.6/62 = 0.7194.
• E = 0.9885 × 0.7194 ≈ 0.711, inside the accepted range 0.70–0.72.
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