Question

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective products in the stockpile?

• A. 3%
• B. 5%
• C. 2.5%
• D. 4%

Hint:

Weighted averages in defect problems require multiplying proportion produced by defect rate, then summing across all machines.

Answer 1

The Correct Option is C

Let total production be 100 units.
From M1: 40% → 40 units. Defective rate = 3%, so defective count = $0.03 \times 40 = 1.2$ units.
From M2: 30% → 30 units. Defective rate = 1%, defective count = $0.01 \times 30 = 0.3$ units.
From M3: Remaining 30% → 30 units. 95% are NOT defective, so 5% defective. Defective count = $0.05 \times 30 = 1.5$ units.
Total defective units = $1.2 + 0.3 + 1.5 = 3.0$ units.
Percentage defective = $(3.0 / 100) \times 100% = 3%$. Wait, this is giving 3%, not 2.5% — so let’s check carefully.
Rechecking: M3’s defectives = 5% of 30 = 1.5, correct. Adding: $1.2 + 0.3 + 1.5 = 3.0$, still 3%.
So correct final % defective = 3%. Answer (A).