Caselet

Three machines M1, M2, and M3 produce 1,000 items a day in total. M1 produces 30% of the total, and M2 produces 100 more items than M3. The defect rates are 2% for M1, 3% for M2, and 5% for M3.

Question

What percentage of the day's total production is defective?

Table built from the caselet

Solution

1. M1 = 30% of 1,000 = 300, so M2 + M3 = 700.
2. With M2 = M3 + 100: 2 x M3 + 100 = 700, so M3 = 300 and M2 = 400.
3. Defective items: 2% of 300 = 6; 3% of 400 = 12; 5% of 300 = 15; total = 33.
4. Defective percentage = 33 / 1,000 x 100 = 3.3%.