A factory producing locks has two quality control managers, Harold and

Let the number of locks examined by Harold = x

Then the number of errors made by Harold = 0.08% of x = 0.0008x

Let the number of locks examined by Sylvia = y

Then the number of errors made by Sylvia = 0.05% of y = 0.0005y

Given that the % of combined errors i.e \(\frac{Errors \space by \space Harold \space+\space Errors \space by \space Sylvia }{ Total \space locks \space Inspected}\) = 0.075%

\(\frac{0.0008x + 0.0005y}{x + y} = 0.00075\)

0.0008x + 0.0005y = 0.00075x + 0.00075y

Multiplying by 10000, we get 8x + 5y = 7.5x + 7.5y

0.5x = 2.5y

x = 5y

Fraction of locks examined by Sylvia = \(\frac{y}{x+y} = \frac{y}{5y + y} = \frac{y}{6y} = \frac{1}{6}\)


Option A

Arun Kumar