Question

In a factory there are three types of Machines $M_1,M_2$ and $M_3$ which produces $25\%$, $35\%$ and $40\%$ of the total products respectively. $M_1,M_2$ and $M_3$ produces $2\%$, $4\%$ and $5\%$ defective products, respectively. What is the percentage of non-defective products?

• A. $89\%$
• B. $97.1\%$
• C. $96.1\%$
• D. $86.1\%$

Answer 1

Answer: (C)

$96.1\%$

Given the machine $M_1$ produces 25% of the total products and 2% defective products

Then, machine $M_1$'s non-defective products $=\frac{25\times \frac{98}{100}}{100}=\frac{25\times 0.98}{100}$

Given the machine $M_2$ produces 35% of the total products and 4% defective products

Then, machine $M_2$'s non-defective products $=\frac{35\times \frac{96}{100}}{100}=\frac{35\times 0.96}{100}$

Given the machine $M_3$ produces 40% of the total products and 5% defective products

Then, machine $M_3$'s non-defective products $=\frac{40\times \frac{95}{100}}{100}=\frac{25\times 0.95}{100}$

Then, $\%$ of non-defective products $=\frac{25\times 0.98+35\times 0.96\times 40\times 0.95}{100}\times 100=24.5+33.6+38=96.1$%