A quality control officer tracks the defect rates in 4 different machines in a textile factory. The first machine produces fabrics with an average defect rate of 1.8%, the second with 2.4%, and the third with 1.6%. The fourth machine operated for 5 fewer hours than the average runtime of the first three, yet its total defective output was 0.92 units. If the total number of defective units from all four machines is 4.12, and each machine’s total production was identical, find the defect percentage of the fourth machine.
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Correct answer: C
Explanation
Given:
First machine defect % = 1.8
Second machine defect % = 2.4
Third machine defect % = 1.6
Defective units of all four machines = 4.12
Defective units of the fourth machine = 0.92
Production of all machines is the same
Defective units of the first three machines = 4.12 − 0.92 = 3.20
Total defect % of the first three machines = 1.8 + 2.4 + 1.6 = 5.8%
Let the production of each machine = x
(1.8/100)x + (2.4/100)x + (1.6/100)x = 3.20
(5.8/100)x = 3.20
x = 55.17
Defect % of the fourth machine = (0.92 / 55.17) × 100 = 1.67%